l probability (A-level only) Flashcards","topicId":"9f048f91-2f32-42c9-abee-a502c8b41066","topicSlug":"conditional-probability","cards":[{"id":"1e2d124a-74ca-4bc8-a811-11e42ccedb5b","cardType":"basic","front":"What event does $A\\cap B$ represent?","back":"Both $A$ and $B$ occur.","points":1,"mcqOptions":null},{"id":"16b52ee8-eb9b-467e-8814-b347e8eadadd","cardType":"basic","front":"In $P(A\\mid B)$, which event becomes the reduced sample space?","back":"Event $B$.","points":1,"mcqOptions":null},{"id":"5d737fcb-c7b6-467f-b832-405a4c632c5e","cardType":"basic","front":"What does the vertical line in $P(A\\mid B)$ mean?","back":"Given that.","points":1,"mcqOptions":null},{"id":"9d378812-7956-4d20-8476-772baa2d78f4","cardType":"basic","front":"Why must $P(B)>0$ when calculating $P(A\\mid B)$?","back":"The formula divides by $P(B)$, and division by zero is undefined.","points":2,"mcqOptions":null},{"id":"12b171d6-c65d-440f-b2b5-0cb4158fb298","cardType":"cloze","front":"In $P(A\\mid B)$, the denominator is $\\text{[...]}$ and the numerator is $P(A\\cap B)$.","back":"In $P(A\\mid B)$, the denominator is $\\boxed{P(B)}$ and the numerator is $P(A\\cap B)$.","points":null,"mcqOptions":null},{"id":"6b13ef4e-67c7-4c90-9d2b-61383bf7017c","cardType":"cloze","front":"In $P(A\\mid B)$, the denominator is $P(B)$ and the numerator is $\\text{[...]}$.","back":"In $P(A\\mid B)$, the denominator is $P(B)$ and the numerator is $\\boxed{P(A\\cap B)}$.","points":null,"mcqOptions":null},{"id":"23d74e84-1da9-40e7-aeca-feaf4bf34818","cardType":"basic","front":"A picture card is selected from a standard pack. What is $P(\\text{king}\\mid\\text{picture card})$?","back":"$\\frac{4}{12}=\\frac{1}{3}$","points":1,"mcqOptions":null},{"id":"03bd457c-c1d2-460c-b859-e37778a54aad","cardType":"basic","front":"Given $P(A\\cap B)=0.3$ and $P(B)=0.5$, calculate $P(A\\mid B)$.","back":"$\\frac{0.3}{0.5}=0.6$","points":1,"mcqOptions":null},{"id":"f931393e-b9c4-4641-b114-929819bad9a2","cardType":"cloze","front":"The conditional probability formula is $\\text{[...]}$, provided that $P(B)>0$.","back":"The conditional probability formula is $\\boxed{P(A\\mid B)=\\frac{P(A\\cap B)}{P(B)}}$, provided that $P(B)>0$.","points":null,"mcqOptions":null},{"id":"14581359-6b0a-4e48-b7e4-e9f440546b48","cardType":"cloze","front":"The conditional probability formula is $P(A\\mid B)=\\frac{P(A\\cap B)}{P(B)}$, provided that $\\text{[...]}$.","back":"The conditional probability formula is $P(A\\mid B)=\\frac{P(A\\cap B)}{P(B)}$, provided that $\\boxed{P(B)>0}$.","points":null,"mcqOptions":null},{"id":"9057bf19-26e1-495b-93bb-709a3098dfe4","cardType":"basic","front":"Rearrange the conditional probability formula to make $P(A\\cap B)$ the subject.","back":"$P(A\\cap B)=P(B)P(A\\mid B)$","points":1,"mcqOptions":null},{"id":"b50f70e7-1385-4429-a31a-16fd87689194","cardType":"basic","front":"Why are $P(A\\mid B)$ and $P(B\\mid A)$ generally unequal?","back":"They use different reduced sample spaces and denominators.","points":2,"mcqOptions":null},{"id":"35496693-bdd7-43a0-b401-dc1e793b666d","cardType":"basic","front":"On a probability tree, what must branches leaving the same point sum to?","back":"$1$","points":1,"mcqOptions":null},{"id":"aeb9af02-062c-4946-b714-6869b90e1526","cardType":"basic","front":"How is the probability of a complete route through a tree found?","back":"Multiply the probabilities along its branches.","points":1,"mcqOptions":null},{"id":"b381fbf4-7a94-45ea-ad0f-6375a26138b9","cardType":"basic","front":"How are probabilities combined when separate tree routes produce the required event?","back":"Add the probabilities of the suitable routes.","points":1,"mcqOptions":null},{"id":"7504a702-9f0c-40a0-b558-bf269a7c594f","cardType":"basic","front":"A bag has three red and two blue counters. Without replacement, what is $P(\\text{second blue}\\mid\\text{first red})$?","back":"$\\fra

2.3.2 Conditional probability (A-level only) Flashcards

2.3.2 Conditional probability (A-level only) Flashcards