l probability (A-level only) Flashcards","topicId":"3ea9780e-1e82-432a-a963-847807997a81","topicSlug":"conditional-probability","cards":[{"id":"2492a3fd-ec70-4a4d-bb4b-a6df91273626","cardType":"basic","front":"What does $A\\cap B$ represent?","back":"The event that both $A$ and $B$ occur.","points":1,"mcqOptions":null},{"id":"07a70ce1-6fde-4e74-a87a-9b18062686d0","cardType":"basic","front":"What does $A\\cup B$ represent?","back":"The event that at least one of $A$ or $B$ occurs.","points":1,"mcqOptions":null},{"id":"a7f39eda-998a-4166-b01e-0aa054648046","cardType":"cloze","front":"For any two events, $$\\text{[...]}$$","back":"For any two events, $$\\boxed{P(A\\cup B)=P(A)+P(B)-P(A\\cap B)}$$","points":null,"mcqOptions":null},{"id":"1080202f-d552-4858-a14c-e8769608c210","cardType":"basic","front":"Why is $P(A\\cap B)$ subtracted when calculating $P(A\\cup B)$?","back":"The intersection was counted twice in $P(A)+P(B)$.","points":2,"mcqOptions":null},{"id":"998f3143-aa3a-4615-b455-27a9e6bba127","cardType":"basic","front":"What does $P(A\\mid B)$ mean?","back":"The probability that $A$ occurs, given $B$ has occurred.","points":1,"mcqOptions":null},{"id":"1d597ca4-2614-4897-bd60-08f91e6f8810","cardType":"basic","front":"When conditioning on $B$, what becomes the restricted sample space?","back":"The event $B$.","points":1,"mcqOptions":null},{"id":"110ec0b8-2681-4305-81de-d951bcd18011","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":"cb53139f-dfd4-45a7-8880-56d62e6216cc","cardType":"basic","front":"Which probability is the denominator in $P(A\\mid B)$?","back":"The probability of the given event: $P(B)$.","points":1,"mcqOptions":null},{"id":"d406d32e-179e-47b6-ae13-0108c03691fe","cardType":"basic","front":"Why are $P(A\\mid B)$ and $P(B\\mid A)$ generally unequal?","back":"They use different restricted sample spaces and denominators.","points":2,"mcqOptions":null},{"id":"d8b3c962-e507-4b4d-aa42-7ee199c6c1e6","cardType":"basic","front":"Given $P(A\\cap B)=0.3$ and $P(B)=0.5$, calculate $P(A\\mid B)$.","back":"$P(A\\mid B)=0.6$.","points":2,"mcqOptions":null},{"id":"fe2245ae-8a00-4692-b425-69167abedc66","cardType":"cloze","front":"The multiplication rule is $$\\text{[...]}$$","back":"The multiplication rule is $$\\boxed{P(A\\cap B)=P(A)P(B\\mid A)}$$","points":null,"mcqOptions":null},{"id":"f1c063a2-0dc9-431b-a123-87bbc99cb570","cardType":"basic","front":"If $P(M)=0.55$ and $P(F\\mid M)=0.40$, find $P(M\\cap F)$.","back":"$0.55\\times0.40=0.22$.","points":2,"mcqOptions":null},{"id":"9fcba342-f614-4a40-8985-a968aa15896e","cardType":"cloze","front":"Probabilities on branches leaving the same point of a tree must [ ].","back":"Probabilities on branches leaving the same point of a tree must add to 1.","points":null,"mcqOptions":null},{"id":"d7da4dfc-678d-452f-b9a0-36e0b6835e82","cardType":"basic","front":"How is the probability of one complete route through a tree found?","back":"Multiply the probabilities along its branches.","points":1,"mcqOptions":null},{"id":"d363bbc1-8739-444b-9e6e-6e17a385dbf0","cardType":"basic","front":"How are mutually exclusive tree routes leading to the same event combined?","back":"Add their route probabilities.","points":1,"mcqOptions":null},{"id":"59da6a87-1558-4175-9387-6715c43f4450","cardType":"basic","front":"How are branch probabilities updated after an object is removed without replacement?","back":"

Reduce the total by one.
Reduce the removed category count by one.

","points":2,"mcqOptions":null},{"id":"9e283b4e-56f8-4db3-9850-8d4ac703a036","cardType":"basic","front":"Three red and two blue counters are sampled

2.3.3 Conditional probability (A-level only) Flashcards

2.3.3 Conditional probability (A-level only) Flashcards