Conditional Probability

Front

What is Conditional Probability?

Back

The probability of an event occurring given that another event has already occurred.

Front

What is the formula for Conditional Probability?

Back

P(A|B) = \frac{P(A \cap B)}{P(B)} where P(A|B) is the probability of A given B.

Front

Define Independent Events.

Back

Two events are independent if the occurrence of one does not affect the occurrence of the other.

Front

Define Dependent Events.

Back

Two events are dependent if the occurrence of one event affects the occurrence of the other.

Front

What is the probability of selecting a pizza and water together, P(Pizza ∩ Water)?

Back

P(Pizza ∩ Water) = \frac{58}{400}.

Front

What does P(Sandals|Pants) represent?

Back

The probability of selecting sandals given that pants have been selected.

Front

What is the probability that a randomly selected student plays sports given that they do not do community service?

Back

P(Sports | No Community Service) = \frac{4}{12}.

Front

If P(A) = 0.3 and P(B) = 0.5, what is P(A ∩ B) if A and B are independent?

Back

P(A ∩ B) = P(A) * P(B) = 0.3 * 0.5 = 0.15.

Front

What is the complement of an event?

Back

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

Front

What is the Law of Total Probability?

Back

If B1, B2, ..., Bn are disjoint events that cover the sample space, then P(A) = \sum_{i=1}^{n} P(A|Bi)P(Bi).