AP Stats - Chapter 14 Probability

Front

What is the formula for calculating the probability of the intersection of two events, A and B?

Back

P(A ∩ B) = P(A) * P(B) if A and B are independent.

Front

How do you calculate conditional probability, P(A|B)?

Back

P(A|B) = P(A ∩ B) / P(B) where P(B) > 0.

Front

What does it mean for two events to be independent?

Back

Two events A and B are independent if the occurrence of one does not affect the occurrence of the other, i.e., P(A ∩ B) = P(A) * P(B).

Front

What is the probability of the complement of an event A, denoted as P(A^C)?

Back

P(A^C) = 1 - P(A).

Front

How do you find the probability of the union of two events, A and B?

Back

P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Front

What is a tree diagram and how is it used in probability?

Back

A tree diagram is a visual representation of all possible outcomes of an event, used to calculate probabilities of compound events.

Front

If P(A) = 0.2 and P(B) = 0.4, what is P(A ∩ B^C)?

Back

P(A ∩ B^C) = P(A) * P(B^C) = P(A) * (1 - P(B)) = 0.2 * 0.6 = 0.12.

Front

What is the probability of two events A and B occurring together if they are not independent?

Back

P(A ∩ B) must be calculated using the specific relationship between A and B, not simply P(A) * P(B).

Front

How do you interpret the result of P(Pants ∩ Shoes) = 10/36?

Back

This means that the probability of randomly selecting an item that is both Pants and Shoes is 10 out of 36 total outcomes.

Front

What does P(Sandals|Pants) = 2/7 indicate?

Back

This indicates that given the condition of having Pants, the probability of also having Sandals is 2 out of 7.