shcards","topicId":"00083bf1-ce71-4e5f-b0e4-52201a555a04","topicSlug":"probability-6","cards":[{"id":"313ddc29-1b8c-4d14-b6bf-431c5a4c778d","cardType":"cloze","front":"For any event $A$, $\\text{[...]}$.","back":"For any event $A$, $\\boxed{0\\le P(A)\\le 1}$.","points":null,"mcqOptions":null},{"id":"bea135ba-557b-4012-8d0b-531d48ae206e","cardType":"cloze","front":"The complement rule is $\\text{[...]}$.","back":"The complement rule is $\\boxed{P(A')=1-P(A)}$.","points":null,"mcqOptions":null},{"id":"983272bf-b7bd-4b78-bc35-ec4fbd9f5bc9","cardType":"basic","front":"Which notation represents “$A$ and $B$”?","back":"$A\\cap B$","points":1,"mcqOptions":null},{"id":"ad3568fd-e859-44dc-89bd-e156396e60cd","cardType":"basic","front":"Which notation represents inclusive “$A$ or $B$”?","back":"$A\\cup B$","points":1,"mcqOptions":null},{"id":"6b55497e-ad99-474f-9bdf-75ad56b077b0","cardType":"cloze","front":"The addition rule is $\\text{[...]}$.","back":"The addition rule is $\\boxed{P(A\\cup B)=P(A)+P(B)-P(A\\cap B)}$.","points":null,"mcqOptions":null},{"id":"0c9ccab7-1454-43f3-b1a7-14dd114b1260","cardType":"basic","front":"Why is $P(A\\cap B)$ subtracted in the addition rule?","back":"The intersection was counted twice.","points":2,"mcqOptions":null},{"id":"cb286f46-a968-4025-ad66-785ce4481bc2","cardType":"basic","front":"When $B$ is known to have occurred, which outcomes remain possible?","back":"Only outcomes inside $B$.","points":1,"mcqOptions":null},{"id":"3ed6dc8e-ca5d-41ff-bc7e-9375ad094cb9","cardType":"cloze","front":"Provided $P(B)>0$, $\\text{[...]}$.","back":"Provided $P(B)>0$, $\\boxed{P(A\\mid B)=\\frac{P(A\\cap B)}{P(B)}}$.","points":null,"mcqOptions":null},{"id":"7720fc23-0666-409e-81e9-fc90c8a5c545","cardType":"basic","front":"What is the denominator when calculating $P(A\\mid B)$?","back":"$P(B)$, the probability of the given event.","points":1,"mcqOptions":null},{"id":"63bb607a-b680-47ef-b68c-5ee66c33c6ec","cardType":"basic","front":"Given $P(M)=0.45$ and $P(P\\cap M)=0.18$, calculate $P(P\\mid M)$.","back":"$0.4$","points":2,"mcqOptions":null},{"id":"82901cbe-6f17-4ac1-a738-47ccd64cc133","cardType":"cloze","front":"The multiplication rule is $\\text{[...]}$.","back":"The multiplication rule is $\\boxed{P(A\\cap B)=P(B)P(A\\mid B)}$.","points":null,"mcqOptions":null},{"id":"5acaeaa4-ae48-4f19-b8ab-b4116b0efa60","cardType":"basic","front":"What must probabilities on branches leaving the same point total?","back":"$1$","points":1,"mcqOptions":null},{"id":"e9efb356-a673-4aae-b778-596675c19939","cardType":"basic","front":"How do you find the probability of one complete route through a tree diagram?","back":"Multiply along its branches.","points":1,"mcqOptions":null},{"id":"3da67d54-50c5-4be1-b303-0e842bc44851","cardType":"basic","front":"How do you combine separate tree routes producing the same required event?","back":"Add their probabilities.","points":1,"mcqOptions":null},{"id":"28c6517b-3a8f-4120-93d5-64fa6a54a52b","cardType":"basic","front":"A student takes a bus with probability $0.6$ or walks with probability $0.4$. Their late probabilities are $0.2$ and $0.1$ respectively. Find $P(L)$.","back":"$P(L)=(0.6)(0.2)+(0.4)(0.1)=0.16$","points":3,"mcqOptions":null},{"id":"9c400db7-f3d5-407b-a433-ff1cbc5fb225","cardType":"basic","front":"Given $P(B\\cap L)=0.12$ and $P(L)=0.16$, calculate $P(B\\mid L)$.","back":"$\\frac{0.12}{0.16}=\\frac34$","points":2,"mcqOptions":null},{"id":"9163d4ea-74a9-4f88-ad4b-f34af599999c","cardType":"basic","front":"How is $P(A\\mid B)$ found from frequencies in a Venn diagram?","back":"$\\frac{\\text{frequency in }A\\cap B}{\\text{frequency in }B}$","points":2,"mcqOptions":null},{"id":"4d387211-fc0e-447a-9638-a6b493eee1c7","cardType":"basic","front":"In a two-way table, 36 people attended and passed, while 50 passed overall. Find $P(\\text{attended}\\mid\\text{passed})$.","back":"

4.4.1 Probability (A-level only) Flashcards

4.4.1 Probability (A-level only) Flashcards