range of values can a probability $P(A)$ take?","back":"$$0 \\le P(A) \\le 1$","points":1},{"id":"4cde314a-63bb-42a7-b01c-9b20ffb3f524","cardType":"cloze","front":"For any event $A$, the probability of its complement $A'$ is calculated as $P(A') = \\text{[...]}$.","back":"For any event $A$, the probability of its complement $A'$ is calculated as $P(A') = \\boxed{1 - P(A)}$.","points":null},{"id":"3b459ebe-3bbf-43ca-91bc-b82c7cfaee95","cardType":"basic","front":"In set notation, what symbol represents the intersection (A and B)?","back":"$$A \\cap B$","points":1},{"id":"6f66d336-523c-42b5-8a8f-2262c2f4c0ec","cardType":"basic","front":"In set notation, what symbol represents the union (A or B)?","back":"$$A \\cup B$","points":1},{"id":"28b4c312-2c89-4e16-b935-c73adb553f6c","cardType":"basic","front":"In a Venn diagram, why is $P(A \\cap B)$ subtracted in the formula for $P(A \\cup B)$?","back":"To avoid double-counting the overlap between the two events.","points":2},{"id":"426eff3c-b3bd-4724-b8ae-538fe83d0973","cardType":"cloze","front":"The addition rule for the union of two events is $P(A \\cup B) = \\text{[...]}$.","back":"The addition rule for the union of two events is $P(A \\cup B) = \\boxed{P(A) + P(B) - P(A \\cap B)}$.","points":null},{"id":"fb58a8d7-bb47-4b6a-aeca-da8d594abcc6","cardType":"basic","front":"Define mutually exclusive events.","back":"Events that cannot happen at the same time.","points":1},{"id":"03ba26e2-17f1-4a01-87e5-2af9adbf0c94","cardType":"cloze","front":"If events $A$ and $B$ are mutually exclusive, then $P(A \\cap B) = \\text{[...]}$.","back":"If events $A$ and $B$ are mutually exclusive, then $P(A \\cap B) = \\boxed{0}$.","points":null},{"id":"4544c671-ea9b-4e36-b5b9-5d68f62c2ae1","cardType":"basic","front":"If two events are mutually exclusive and have non-zero probabilities, can they be independent?","back":"No; knowing one occurs makes the other impossible, so they affect each other.","points":2},{"id":"0e4bd064-46a5-4703-a2fc-e9147a0858c6","cardType":"basic","front":"What is the first step when filling in a three-set Venn diagram?","back":"Place the value for the center region (all three events) first.","points":1},{"id":"627b56bb-61b5-4e7d-a28f-b34d0fdb53fa","cardType":"basic","front":"Define independent events.","back":"The outcome of one event does not affect the probability of the other.","points":1},{"id":"6525d840-acc4-4147-9cb7-f86ddfa4d546","cardType":"cloze","front":"Events $A$ and $B$ are independent if and only if $P(A \\cap B) = \\text{[...]}$.","back":"Events $A$ and $B$ are independent if and only if $P(A \\cap B) = \\boxed{P(A)P(B)}$.","points":null},{"id":"b6cfee48-238d-428e-9ea3-c9b0746fef61","cardType":"basic","front":"When asked to test for independence in an exam, what must your answer include?","back":"A comparison showing whether $P(A \\cap B)$ equals $P(A)P(B)$.","points":2},{"id":"2c507209-94e7-4cda-8dee-bd0c30b27677","cardType":"basic","front":"In a tree diagram, how do you calculate the probability of a specific combined outcome (e.g., A and then B)?","back":"Multiply the probabilities along the branches.","points":1},{"id":"64a193c5-bf4a-4eed-a00f-e86e8ea1d5ce","cardType":"cloze","front":"When multiple different routes on a tree diagram satisfy a condition, you [ ] their individual probabilities.碎","back":"When multiple different routes on a tree diagram satisfy a condition, you add their individual probabilities.碎","points":null},{"id":"36509c19-31ce-47c0-a864-a7f08304024f","cardType":"basic","front":"What does the notation $P(B|A)$ represent?","back":"The conditional probability of $B$ given that $A$ has occurred.","points":1},{"id":"3f3c824a-9f2d-43f5-b178-c87858a891cd","cardType":"basic","front":"How does \"without replacement\" affect a tree

Probability Flashcards

Probability Flashcards

Probability Flashcards

Probability Flashcards