32:I[196793,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/3do_93-6buld5.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790362613","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613"],"Gingerbread"] 34:I[647935,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/3do_93-6buld5.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790362613","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613"],"RecordResourceResume"] 35:I[830476,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/3do_93-6buld5.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790362613","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613"],"FlashcardAccessBranch"] 36:I[315438,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/3do_93-6buld5.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/3h4suq-9gmzwh.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/1gtlwpzgzi12z.js?dpl=nogit-1790362613","/_next/static/chunks/2zwoemojbdlmi.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/120-bka6zq5lp.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613"],"TopicFlashcardRunner"] 23:[["$","$L32",null,{"feature":"flashcards"}],"$L33",["$","$L34",null,{"href":"/gcse/maths/aqa/grade-2-2-12-probability/flashcards","label":"Probability","subjectCode":"gcse_maths__aqa","surface":"flashcards"}],["$","$L35",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L36",null,{"decks":[{"id":"7b7d9f2f-36f3-11b4-d537-3d89bfaaee2c","title":"Probability Flashcards","topicId":"b34da82c-8d1e-421c-b24d-0884d5b98a93","topicSlug":"grade-2-2-12-probability","cards":[{"id":"44c59d89-7e0b-ad31-e03e-514eab0b465b","cardType":"basic","points":1,"front":"What interval must every probability lie in?","back":"From 0 to 1 inclusive.","mcqOptions":[{"text":"From 0 to 1 inclusive.","correct":true,"explanation":"A probability cannot be less than 0 or greater than 1. Probability 0 represents an impossible event, while probability 1 represents a certain event."},{"text":"From -1 to 1 inclusive.","correct":false,"explanation":"Including negative values confuses probability with scales that permit signed numbers. Every probability lies from 0 to 1 inclusive, because chances cannot be below impossibility."},{"text":"From 0 to 0.5 inclusive.","correct":false,"explanation":"This excludes probabilities greater than one half, including likely and certain events. The correct interval is from 0 to 1 inclusive."},{"text":"From 0 to 100 inclusive.","correct":false,"explanation":"Probabilities are not percentages unless converted, so the upper bound is 1 rather than 100. The correct interval is from 0 to 1 inclusive."}]},{"id":"ec7681fd-2705-023c-995d-6a5a8d6faba3","cardType":"cloze","points":null,"front":"Rolling a 5 is an [ ]; rolling an even number is an [ ].","back":"Rolling a 5 is an outcome; rolling an even number is an event.","mcqOptions":[{"text":"Rolling a 5 is an outcome; rolling an even number is an event.","correct":true,"explanation":"An outcome is one specific possible result, such as rolling 5. An event is a set of outcomes, such as rolling any even number."},{"text":"Rolling a 5 is an event; rolling an even number is an outcome.","correct":false,"explanation":"This reverses the definitions. Rolling 5 is one specific outcome, whereas rolling an even number describes the event containing outcomes 2, 4 and 6."},{"text":"Rolling a 5 is a trial; rolling an even number is an outcome.","correct":false,"explanation":"A trial is the action of rolling the die, not the result obtained. Rolling 5 is an outcome, while rolling an even number is an event."},{"text":"Rolling a 5 is a sample space; rolling an even number is a sample space.","correct":false,"explanation":"A sample space contains all possible results, so neither description is a sample space. Rolling 5 is an outcome, and rolling an even number is an event."}]},{"id":"9053cdce-6d4f-f893-c733-a180ed5228f5","cardType":"cloze","points":null,"front":"A result that is not chosen on purpose is [ ].","back":"A result that is not chosen on purpose is at random.","mcqOptions":[{"text":"at random","correct":true,"explanation":"A result obtained without deliberately selecting it is described as being at random. Random selection is intended to avoid purposeful choice influencing the result."},{"text":"biased","correct":false,"explanation":"A biased result is affected by an unfair method or unequal chances, not merely unchosen. A result not chosen on purpose is described as being at random."},{"text":"systematic","correct":false,"explanation":"A systematic result follows a planned rule or pattern, which conflicts with selection without purposeful choice. The required description is at random."},{"text":"certain","correct":false,"explanation":"A certain result must occur, whereas lack of purposeful selection does not guarantee any particular result. The correct description is at random."}]},{"id":"a7896097-657d-143a-11ba-f8e684744770","cardType":"cloze","points":null,"front":"If each outcome has the same chance, the outcomes are [ ].","back":"If each outcome has the same chance, the outcomes are equally likely.","mcqOptions":[{"text":"equally likely","correct":true,"explanation":"Outcomes are equally likely when every one has the same probability of occurring. For example, each face of a fair six-sided die has probability $\\frac{1}{6}$."},{"text":"unequally likely","correct":false,"explanation":"Unequally likely means that some outcomes have different probabilities, directly contradicting the condition that each has the same chance. The outcomes are equally likely."},{"text":"certain","correct":false,"explanation":"Certain means having probability 1, rather than sharing the same chance with other possible outcomes. Outcomes with the same probability are equally likely."},{"text":"impossible","correct":false,"explanation":"Impossible outcomes each have probability 0 and cannot occur; equal non-zero chances are not described this way. Outcomes with the same chance are equally likely."}]},{"id":"35d04be8-de82-9b6e-aa85-150e1c7fbfc0","cardType":"basic","points":1,"front":"For equally likely outcomes, what calculation gives the probability of an event?","back":"$\\frac{\\text{wanted outcomes}}{\\text{total outcomes}}$","mcqOptions":[{"text":"$\\frac{\\text{wanted outcomes}}{\\text{total outcomes}}$","correct":true,"explanation":"For equally likely outcomes, probability is found by dividing the number of outcomes that satisfy the event by the total number of possible outcomes."},{"text":"$\\frac{\\text{total outcomes}}{\\text{wanted outcomes}}$","correct":false,"explanation":"Reversing the fraction can produce a value greater than 1, which cannot be a probability. Divide wanted outcomes by total outcomes instead."},{"text":"$\\frac{\\text{unwanted outcomes}}{\\text{total outcomes}}$","correct":false,"explanation":"This calculates the probability of the complementary event by counting outcomes that are not wanted. The required probability uses wanted outcomes over total outcomes."},{"text":"$\\frac{\\text{wanted outcomes}}{\\text{unwanted outcomes}}$","correct":false,"explanation":"Comparing wanted outcomes only with unwanted outcomes omits part of the sample space from the denominator. The denominator must be the total number of outcomes."}]},{"id":"15fd81a1-24e7-351c-3b58-3b84fdb1c305","cardType":"basic","points":1,"front":"Cards show 2, 4, 4, 5, 7, 8, 9. What is the probability of picking a 4?","back":"$\\frac{2}{7}$","mcqOptions":[{"text":"$\\frac{2}{7}$","correct":true,"explanation":"There are seven cards in total and two of them show 4. Therefore, the probability of selecting a 4 is $\\frac{2}{7}$."},{"text":"$\\frac{1}{7}$","correct":false,"explanation":"This counts the value 4 only once because it treats repeated values as a single outcome. Two of the seven cards show 4, giving $\\frac{2}{7}$."},{"text":"$\\frac{2}{6}$","correct":false,"explanation":"This incorrectly removes one of the two matching cards from the total after counting it. All seven cards remain possible selections, so the probability is $\\frac{2}{7}$."},{"text":"$\\frac{4}{7}$","correct":false,"explanation":"This uses the number printed on the desired cards as the numerator instead of counting those cards. There are two matching cards out of seven, giving $\\frac{2}{7}$."}]},{"id":"f8cfc698-34e0-8e64-03f2-3d84dad865cd","cardType":"cloze","points":null,"front":"On a probability scale, 0 means [ ] and 1 means [ ].","back":"On a probability scale, 0 means impossible and 1 means certain.","mcqOptions":[{"text":"On a probability scale, 0 means impossible and 1 means certain.","correct":true,"explanation":"Probability 0 represents an event that cannot happen, so it is impossible. Probability 1 represents an event that must happen, so it is certain."},{"text":"On a probability scale, 0 means certain and 1 means impossible.","correct":false,"explanation":"This reverses the endpoints of the probability scale. Probability 0 means impossible because the event cannot occur, while probability 1 means certain."},{"text":"On a probability scale, 0 means unlikely and 1 means likely.","correct":false,"explanation":"Unlikely and likely describe probabilities near the endpoints, not exactly at them. Probability 0 means impossible, and probability 1 means certain."},{"text":"On a probability scale, 0 means an even chance and 1 means an even chance.","correct":false,"explanation":"An even chance corresponds to probability $\\frac{1}{2}$, so it cannot describe either endpoint. At 0 an event is impossible, and at 1 it is certain."}]},{"id":"cbf6f267-2731-352f-4e79-cd6c2c557387","cardType":"cloze","points":null,"front":"On a probability scale, [ ] means an even chance.","back":"On a probability scale, $\\frac{1}{2}$ means an even chance.","mcqOptions":[{"text":"$$\\frac{1}{2}$","correct":true,"explanation":"An even chance means that an event is equally likely to happen or not happen. Its probability is therefore one half, written $\\frac{1}{2}$."},{"text":"$$0$","correct":false,"explanation":"A probability of 0 represents an impossible event, not an even chance. An event with an even chance has probability $\\frac{1}{2}$."},{"text":"$$1$","correct":false,"explanation":"A probability of 1 represents a certain event, not one equally likely to happen or not happen. An even chance is represented by $\\frac{1}{2}$."},{"text":"$$\\frac{1}{4}$","correct":false,"explanation":"This gives a one-in-four chance, so the event is less likely to happen than not happen. An even chance has probability $\\frac{1}{2}$."}]},{"id":"ebeb7d92-80cb-52ff-f50a-aff6590ced66","cardType":"basic","points":1,"front":"On a probability scale, where is $\\frac{1}{4}$ placed?","back":"Halfway between 0 and $\\frac{1}{2}$.","mcqOptions":[{"text":"Halfway between 0 and $\\frac{1}{2}$.","correct":true,"explanation":"The midpoint of 0 and $\\frac{1}{2}$ is $\\frac{1}{4}$, because half of $\\frac{1}{2}$ is $\\frac{1}{4}$."},{"text":"Halfway between 0 and 1.","correct":false,"explanation":"The midpoint of 0 and 1 is $\\frac{1}{2}$, not $\\frac{1}{4}$. The value $\\frac{1}{4}$ is halfway between 0 and $\\frac{1}{2}$."},{"text":"Halfway between $\\frac{1}{4}$ and $\\frac{1}{2}$.","correct":false,"explanation":"The midpoint of $\\frac{1}{4}$ and $\\frac{1}{2}$ is $\\frac{3}{8}$. The value $\\frac{1}{4}$ is halfway between 0 and $\\frac{1}{2}$."},{"text":"Halfway between 0 and $\\frac{1}{4}$.","correct":false,"explanation":"The midpoint of 0 and $\\frac{1}{4}$ is $\\frac{1}{8}$, which is too small. The value $\\frac{1}{4}$ lies halfway between 0 and $\\frac{1}{2}$."}]},{"id":"746d1ff3-4b4a-e409-cbd3-477a6cd3a168","cardType":"basic","points":1,"front":"On a probability scale, where is $\\frac{3}{4}$ placed?","back":"Halfway between $\\frac{1}{2}$ and 1.","mcqOptions":[{"text":"Halfway between $\\frac{1}{2}$ and 1.","correct":true,"explanation":"The gap from $\\frac{1}{2}$ to 1 is $\\frac{1}{2}$, and moving halfway across it gives $\\frac{1}{2}+\\frac{1}{4}=\\frac{3}{4}$."},{"text":"Halfway between 0 and 1.","correct":false,"explanation":"The midpoint of the full probability scale from 0 to 1 is $\\frac{1}{2}$. The value $\\frac{3}{4}$ is halfway between $\\frac{1}{2}$ and 1."},{"text":"Halfway between 0 and $\\frac{3}{4}$.","correct":false,"explanation":"The midpoint of 0 and $\\frac{3}{4}$ is $\\frac{3}{8}$, not $\\frac{3}{4}$. The correct endpoints are $\\frac{1}{2}$ and 1."},{"text":"Halfway between $\\frac{3}{4}$ and 1.","correct":false,"explanation":"The midpoint of $\\frac{3}{4}$ and 1 is $\\frac{7}{8}$, so this places the point too high. $\\frac{3}{4}$ is halfway between $\\frac{1}{2}$ and 1."}]},{"id":"d8b53e0e-f15c-a8b9-8be7-2bf85065cf1e","cardType":"basic","points":1,"front":"A fair dice is rolled once. What is the probability of rolling an 8?","back":"0","mcqOptions":[{"text":"0","correct":true,"explanation":"A standard fair dice has outcomes 1 to 6, so rolling an 8 is impossible. An impossible event has probability 0."},{"text":"$\\frac{1}{6}$","correct":false,"explanation":"The probability $\\frac{1}{6}$ applies to one possible face, such as rolling a 4. Since 8 is not on a standard dice, its probability is 0."},{"text":"$\\frac{1}{8}$","correct":false,"explanation":"Using 8 as the denominator mistakes the requested number for the number of possible outcomes. A dice has six outcomes and none is 8, so the probability is 0."},{"text":"1","correct":false,"explanation":"A probability of 1 describes a certain event, but rolling an 8 on a standard six-sided dice is impossible. Its probability is therefore 0."}]},{"id":"63d507e0-4ccf-c357-2500-d88761048c4b","cardType":"basic","points":1,"front":"A fair dice is rolled once. What is the probability of rolling a number less than 7?","back":"1","mcqOptions":[{"text":"1","correct":true,"explanation":"Every possible result on a standard dice - 1, 2, 3, 4, 5 or 6 - is less than 7, so the event is certain and has probability 1."},{"text":"$\\frac{5}{6}$","correct":false,"explanation":"This commonly comes from leaving out 6, but 6 is less than 7 and must be included. All six outcomes qualify, giving $\\frac{6}{6}=1$."},{"text":"$\\frac{6}{7}$","correct":false,"explanation":"Using 7 as the denominator confuses the comparison value with the number of dice outcomes. All six possible outcomes are less than 7, so the probability is 1."},{"text":"$\\frac{1}{6}$","correct":false,"explanation":"This counts only one successful outcome, but all six faces are numbered below 7. The event is certain, so its probability is $\\frac{6}{6}=1$."}]},{"id":"d8c0c65a-e487-92dd-2d54-40d4acadae8b","cardType":"basic","points":1,"front":"A fair dice is rolled once. What is the probability of rolling a number greater than 3?","back":"$\\frac{1}{2}$","mcqOptions":[{"text":"$\\frac{1}{2}$","correct":true,"explanation":"The results greater than 3 are 4, 5 and 6. That gives three favourable outcomes out of six, so the probability is $\\frac{3}{6}=\\frac{1}{2}$."},{"text":"$\\frac{1}{3}$","correct":false,"explanation":"This counts only two successful outcomes, often by overlooking 4. The results greater than 3 are 4, 5 and 6, giving $\\frac{3}{6}=\\frac{1}{2}$."},{"text":"$\\frac{2}{3}$","correct":false,"explanation":"This usually comes from including 3 among the successful outcomes. Greater than 3 excludes 3, leaving 4, 5 and 6, so the probability is $\\frac{1}{2}$."},{"text":"$\\frac{3}{5}$","correct":false,"explanation":"The denominator must include all six possible dice outcomes, not only five of them. Three outcomes are greater than 3, so the probability is $\\frac{3}{6}=\\frac{1}{2}$."}]},{"id":"d919226e-5fd0-b4bc-3446-6f43a0d72ed3","cardType":"cloze","points":null,"front":"In probability, less than 3 means 1 and 2, so it [ ].","back":"In probability, less than 3 means 1 and 2, so it excludes 3.","mcqOptions":[{"text":"excludes 3","correct":true,"explanation":"The phrase “less than 3” includes only values strictly below 3. For whole-number dice outcomes, these are 1 and 2, so 3 itself is excluded."},{"text":"includes 3","correct":false,"explanation":"Including 3 confuses “less than” with “less than or equal to”. A strict inequality does not include its boundary value, so less than 3 excludes 3."},{"text":"excludes 2","correct":false,"explanation":"The number 2 is below 3, so it must be included. Less than 3 includes 1 and 2 but excludes the boundary value 3."},{"text":"includes only 3","correct":false,"explanation":"This confuses values below 3 with the value equal to 3. Less than 3 includes 1 and 2 and excludes 3 itself."}]},{"id":"e35712dc-32d7-3c8b-4d45-959929696a1a","cardType":"basic","points":1,"front":"A box has 25 counters: 9 red, 6 blue and the rest green. How many are green?","back":"10","mcqOptions":[{"text":"10","correct":true,"explanation":"The red and blue counters total $9+6=15$. Subtracting these from the 25 counters leaves $25-15=10$ green counters."},{"text":"9","correct":false,"explanation":"This repeats the number of red counters instead of finding the remainder. After accounting for 9 red and 6 blue counters, $25-9-6=10$ are green."},{"text":"15","correct":false,"explanation":"This is the combined number of red and blue counters, not the number of green counters. Subtracting it from 25 gives $25-15=10$ green counters."},{"text":"16","correct":false,"explanation":"This comes from subtracting only the 9 red counters and forgetting the 6 blue counters. Both known colours must be removed, giving $25-9-6=10$."}]},{"id":"b8993097-6ced-da9b-ba1d-2db928894126","cardType":"basic","points":2,"front":"A box has 25 counters: 9 red, 6 blue and the rest green. What is the probability of green?","back":"$\\frac{2}{5}$","mcqOptions":[{"text":"$\\frac{2}{5}$","correct":true,"explanation":"There are $25-9-6=10$ green counters, so the probability is $\\frac{10}{25}$. Dividing numerator and denominator by 5 simplifies this to $\\frac{2}{5}$."},{"text":"$\\frac{3}{5}$","correct":false,"explanation":"This is the probability of selecting a counter that is not green, since there are 15 red or blue counters. Green has probability $\\frac{10}{25}=\\frac{2}{5}$."},{"text":"$\\frac{2}{3}$","correct":false,"explanation":"This incorrectly uses the 15 red and blue counters as the total. The denominator must be all 25 counters, so green has probability $\\frac{10}{25}=\\frac{2}{5}$."},{"text":"$\\frac{2}{25}$","correct":false,"explanation":"This simplifies the numerator from 10 to 2 without also simplifying the denominator. Dividing both parts of $\\frac{10}{25}$ by 5 gives $\\frac{2}{5}$."}]},{"id":"3701741d-a7ff-cd05-f321-5508ee0d3df2","cardType":"basic","points":1,"front":"A bag has 5 red counters and 1 blue counter. What is the probability of red?","back":"$\\frac{5}{6}$","mcqOptions":[{"text":"$\\frac{5}{6}$","correct":true,"explanation":"There are 6 counters altogether, and 5 of them are red. Therefore, the probability of selecting red is $\\frac{5}{6}$."},{"text":"$\\frac{1}{6}$","correct":false,"explanation":"This is the probability of selecting the single blue counter. Red has 5 favourable outcomes out of 6 counters, so its probability is $\\frac{5}{6}$."},{"text":"$\\frac{5}{5}$","correct":false,"explanation":"This uses only the five red counters as the denominator, incorrectly suggesting that every counter is red. The denominator must be the total of 6, giving $\\frac{5}{6}$."},{"text":"$\\frac{6}{5}$","correct":false,"explanation":"This reverses the required fraction, placing the total number above the number of favourable outcomes. Probability is favourable outcomes over total outcomes, so it is $\\frac{5}{6}$."}]},{"id":"776e3863-804a-c3cf-eeca-bbbd5a94db18","cardType":"cloze","points":null,"front":"An event and its complement have probabilities that add to [ ].","back":"An event and its complement have probabilities that add to 1.","mcqOptions":[{"text":"1","correct":true,"explanation":"An event and its complement cover all possible outcomes without overlapping. Their probabilities must therefore add to 1, representing certainty."},{"text":"0","correct":false,"explanation":"A total probability of 0 represents an impossible event, not all possible outcomes. An event and its complement together are certain, so their probabilities add to 1."},{"text":"2","correct":false,"explanation":"Probabilities across all mutually exclusive possible outcomes cannot total 2. An event and its complement exhaust the sample space, so their probabilities add to 1."},{"text":"0.5","correct":false,"explanation":"A total of 0.5 would represent only half of the total probability. An event and its complement include every outcome, so their probabilities add to 1."}]},{"id":"ae2fe7ca-884c-7cbf-a17e-b234eda99243","cardType":"basic","points":1,"front":"A player has probability 0.7 of winning. What is the probability of not winning?","back":"0.3","mcqOptions":[{"text":"0.3","correct":true,"explanation":"Winning and not winning are complementary events, so their probabilities add to 1. Therefore, the probability of not winning is $1 - 0.7 = 0.3$."},{"text":"0.7","correct":false,"explanation":"This repeats the probability of winning rather than finding its complement. Subtracting the winning probability from 1 gives $1 - 0.7 = 0.3$."},{"text":"1.7","correct":false,"explanation":"This adds the winning probability to 1, producing a value greater than the maximum possible probability. The complement is found by $1 - 0.7 = 0.3$."},{"text":"0.03","correct":false,"explanation":"This introduces an unnecessary decimal-place shift after finding the complement. The correct subtraction is $1.0 - 0.7 = 0.3$, not 0.03."}]},{"id":"5224a545-5df4-8b90-35ac-082589e3f47b","cardType":"basic","points":2,"front":"A table shows 6 red, 4 blue, 5 yellow and 3 green counters. What is the probability of not blue?","back":"$\\frac{7}{9}$","mcqOptions":[{"text":"$\\frac{7}{9}$","correct":true,"explanation":"There are 18 counters in total and 14 are not blue. Thus the probability is $\\frac{14}{18}$, which simplifies to $\\frac{7}{9}$."},{"text":"$\\frac{2}{9}$","correct":false,"explanation":"This is the probability of selecting blue, since 4 of the 18 counters are blue. The complement is $1 - \\frac{2}{9} = \\frac{7}{9}$."},{"text":"$\\frac{7}{18}$","correct":false,"explanation":"This correctly identifies 14 non-blue counters but incorrectly uses 36 rather than 18 as the total before simplifying. The correct probability is $\\frac{14}{18} = \\frac{7}{9}$."},{"text":"$\\frac{4}{9}$","correct":false,"explanation":"This uses the 4 blue counters as the numerator while retaining the simplified denominator incorrectly. There are 14 non-blue counters out of 18, giving $\\frac{7}{9}$."}]},{"id":"d8e718ad-cb46-af14-ee4c-97e2370f1e13","cardType":"basic","points":2,"front":"A probability table has red 0.25, blue 0.15 and yellow 0.40. What is the missing green probability?","back":"0.20","mcqOptions":[{"text":"0.20","correct":true,"explanation":"The probabilities must total 1. The known probabilities sum to $0.25 + 0.15 + 0.40 = 0.80$, leaving $1 - 0.80 = 0.20$."},{"text":"0.80","correct":false,"explanation":"This is the sum of the three known probabilities, not the missing probability. Subtracting that sum from 1 gives $1 - 0.80 = 0.20$."},{"text":"0.10","correct":false,"explanation":"This results from an arithmetic error when subtracting the known total from 1. Since the known probabilities total 0.80, the missing probability is 0.20."},{"text":"0.60","correct":false,"explanation":"This subtracts only the red and blue probabilities and overlooks yellow. All known probabilities must be included, so $1 - 0.25 - 0.15 - 0.40 = 0.20$."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Probability","title":"Probability Flashcards","topbar":{"backHref":"/gcse/maths/aqa/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"b34da82c-8d1e-421c-b24d-0884d5b98a93","walled":"$L38"}],"$L39","$L3a"]