AP Statistics Holiday Probability

Front

What does it mean for two events to be independent in probability?

Back

Two events A and B are independent if the occurrence of one does not affect the probability of the other. Mathematically, P(A|B) = P(A) and P(B|A) = P(B).

Front

What does it mean for two events to be mutually exclusive?

Back

Two events A and B are mutually exclusive if they cannot occur at the same time. If A occurs, B cannot occur, and vice versa. Mathematically, P(A and B) = 0.

Front

How do you calculate the expected value of a discrete random variable?

Back

The expected value E(X) is calculated by summing the products of each outcome and its probability: E(X) = Σ [x * P(x)].

Front

What is the formula for conditional probability?

Back

The formula for conditional probability is P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of A given B.

Front

What is Bayes' Theorem?

Back

Bayes' Theorem relates the conditional and marginal probabilities of random events. It states: P(A|B) = [P(B|A) * P(A)] / P(B).

Front

What is the probability of an event not occurring?

Back

The probability of an event A not occurring is given by P(not A) = 1 - P(A).

Front

If P(A) = 0.12 and P(B|A) = 0.95, what is P(A and B)?

Back

P(A and B) = P(A) * P(B|A) = 0.12 * 0.95 = 0.114.

Front

What is the complement of an event?

Back

The complement of an event A, denoted as A', is the event that A does not occur. The probability of the complement is P(A') = 1 - P(A).

Front

How do you find the probability of the union of two events?

Back

The probability of the union of two events A and B is given by P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the expected number of toys made if an elf can make 1, 2, 3, or 4 toys with probabilities 0.1, 0.3, 0.4, and 0.2 respectively?

Back

E(X) = (1 * 0.1) + (2 * 0.3) + (3 * 0.4) + (4 * 0.2) = 2.7.