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altogether and $15$ are red. Since the rest are blue, subtract the red counters from the total:\n\n$$53-15=38$$\n\nSo there are $38$ blue counters. This subtraction earns the **M1** mark.","highlights":[{"text":"15 of the counters are red.\nThe rest of the counters are blue.","location":"specification"}]},{"type":"text","order":1,"title":"Write the probability","content":"Probability is\n\n$$\\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}.$$\n\nA blue counter is favourable, so use $38$ blue counters out of $53$ counters altogether:\n\n$$\\boxed{\\frac{38}{53}}$$\n\nThis is the **A1** answer mark.","highlights":[{"text":"Find the probability that the counter is blue.","location":"specification"}]}]}],"generatedAt":"2026-07-21T03:58:12.254Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"1e13eae7-bf01-456b-a50f-6bd5825f7515","revisionId":"256b700a-31b1-4e49-b92d-95c8644e8229","questionNumber":"16","questionType":"LA","specification":"A draw is being held to win a prize.\n\nBruce buys 17 tickets.\nA total of 350 tickets are in the draw.","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Probability","calculatorUse":null,"isCalculation":true,"parts":[{"id":"a672bd17-8289-46b4-a88e-3853ce1cb6c8","label":"0","content":"Find the probability that Bruce does **not** win the prize.","markscheme":"- $350 - 17 = 333$ M1\n- $\\frac{333}{350}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Calculates the number of losing tickets ($350 - 17 = 333$).","code":"M"},{"id":"p2","marks":1,"description":"Correct probability of $\\frac{333}{350}$.","code":"A"}],"finalAnswers":["333/350"],"generatedAt":"2026-05-06T15:41:33.671Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"complementary_outcomes","label":"Use the complementary outcome","steps":[{"type":"text","order":0,"title":"Identify the unwanted tickets","content":"Bruce can only win with one of his own tickets. Therefore, the tickets that mean he **does not** win are all the tickets not bought by Bruce.","highlights":[{"text":"Bruce buys 17 tickets.","location":"specification"},{"text":"A total of 350 tickets are in the draw.","location":"specification"},{"text":"does **not** win the prize","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=calculation}{\\color{@sky}{350 - 17 = 333}}"},{"text":"There are 333 tickets that do not belong to Bruce."}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"calculation"}]},"order":1,"title":"Count the other tickets","description":"Subtract Bruce's tickets from the total. This correct subtraction earns the M1 mark."},{"type":"text","order":2,"title":"Write the probability","content":"Probability is $\\dfrac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}$. Here, a favourable outcome means a ticket Bruce does not own, so\n\n$$\\boxed{\\frac{333}{350}}$$\n\nThis is already in its simplest form and earns the A1 mark.","highlights":[{"text":"Find the probability that Bruce does **not** win the prize.","location":"specification"}]}]}],"generatedAt":"2026-07-21T04:01:30.793Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"2e996c48-5d48-4458-8ba0-d553afac5476","revisionId":"7c41f417-3a84-4763-ad5a-204854bbb75a","questionNumber":"19","questionType":"LA","specification":"There are some counters in a bag.\n\nThe table shows the number of counters of each colour.\n\n| Colour | Red | Blue | Yellow | Green |\n| :--- | :--- | :--- | :--- | :--- |\n| Number of Counters | 7 | 2 | 5 | 3 |\n\nA counter is taken at random from the bag.","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Probability","calculatorUse":null,"isCalculation":false,"parts":[{"id":"0fa45cf7-0f3c-4141-b031-115b400c6201","label":"a","content":"Write down the probability that the counter is green.","markscheme":"- Total = $7 + 2 + 5 + 3 = 17$\n- $\\frac{3}{17}$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct probability of $\\frac{3}{17}$.","code":"B"}],"finalAnswers":["3/17"],"generatedAt":"2026-05-06T15:41:33.671Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"favourable_over_total","label":"Favourable outcomes over total","steps":[{"type":"text","order":0,"title":"Count all counters","content":"For a probability, first find the **total number of possible counters**. Add every entry in the table:\n\n$$7+2+5+3=17$$\n\nThere are $17$ counters altogether.","highlights":[{"text":"The table shows the number of counters of each colour.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"text":"Probability = favourable outcomes divided by total outcomes."},{"latex":"\\boxed{P(\\text{green})=\\frac{3}{17}}\\quad\\text{B1}"}]},"order":1,"title":"State the probability","description":"The total number of counters has already been found. The favourable outcomes are the green counters."}]}],"generatedAt":"2026-07-21T04:07:16.066Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"95d1cb03-ac48-4c14-8577-ad81f1ad110b","label":"b","content":"Write down the probability that the counter is not blue.","markscheme":"- $\\frac{15}{17}$ B1","marks":1,"order":1,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct probability of $\\frac{15}{17}$.","code":"B"}],"finalAnswers":["15/17"],"generatedAt":"2026-05-06T15:41:33.671Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"complement_probability","label":"Use the complement","steps":[{"type":"text","order":0,"title":"Count all counters","content":"Add the counters: $7+2+5+3=17$, so there are $17$ counters altogether.","highlights":[{"text":"| Number of Counters | 7 | 2 | 5 | 3 |","location":"specification"}]},{"type":"text","order":1,"title":"Exclude blue counters","content":"There are $2$ blue counters, so the number that are **not** blue is $17-2=15$. This is the favourable number of outcomes.","highlights":[{"text":"not blue","location":"specification"}]},{"type":"text","order":2,"title":"Write the probability","content":"Probability is $\\dfrac{\\text{favourable outcomes}}{\\text{total outcomes}}$, so\n\n$$\\boxed{\\frac{15}{17}}$$\n\nThis earns the B1 mark.","highlights":[{"text":"Write down the probability","location":"specification"}]}]}],"generatedAt":"2026-07-21T04:09:00.823Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"igcse_maths__oxford_aqa","summaries":[{"id":"819a9071-9bdf-431a-8632-50b0e3b93351","difficultyBand":null,"calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"54d4ac0a-e1e0-4eeb-bf81-479fea0558e5","difficultyBand":null,"calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"816aaf3c-5578-4d2a-ae83-8d01c4a15fcc","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"452104a6-7c46-4025-aa13-8521070c66cc","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"e690c746-f971-4b32-aeed-c98a913747ae","difficultyBand":null,"calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"da10fc51-2a8b-4af4-a067-40bd63b13498","difficultyBand":null,"calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"2a3e03b9-59cf-4a46-b99f-47cdc72afd18","difficultyBand":null,"calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"a254884f-c0b5-40aa-a14e-06877360bd34","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"e0371be7-c52e-4344-93d1-636991aada74","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":true},{"id":"34d01b60-24a6-46aa-a59e-ff3edc26a9d4","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":true},{"id":"f9fe9adb-390a-46ee-8fe7-e2d680a1c64d","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"9b97d7c8-b868-45dd-87bb-4afc94d7226d","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"6d830300-1b34-421c-b8da-e4fb50921028","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"1e13eae7-bf01-456b-a50f-6bd5825f7515","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"acdef4de-fad6-4849-a38c-b3e32e2cc637","difficultyBand":null,"calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"2e996c48-5d48-4458-8ba0-d553afac5476","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"6a41e109-3c67-4a7d-9111-b59219645341","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false},{"id":"7f520358-f4bd-445b-b1ce-c637b46aa8f1","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":false}],"title":"Probability","topicId":"16944bc4-5d66-4672-8d47-f52e4a84b6d7","topicSidebar":"$L3a","topicSlug":"grade-2-2-12-probability","topicTitle":"Probability"}]}],"$L3b","$L3c"]}]

Probability

Question 9

Probability Questions

Probability

Question 9

Probability Questions