Conditional Probability

Front

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

Back

Conditional Probability

Front

What is the formula for conditional probability?

Back

P(A|B) = P(A and B) / P(B) where P(A|B) is the probability of A given B.

Front

If P(A) = 1/2 and P(B) = 1/4, what is P(A and B) if A and B are independent?

Back

P(A and B) = P(A) * P(B) = (1/2) * (1/4) = 1/8.

Front

What does it mean for two events to be independent?

Back

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

Front

If P(A) = 1/3 and P(B|A) = 1/2, what is P(A and B)?

Back

P(A and B) = P(A) * P(B|A) = (1/3) * (1/2) = 1/6.

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'.

Front

If P(A) = 3/5, what is P(A')?

Back

P(A') = 1 - P(A) = 1 - 3/5 = 2/5.

Front

What is Bayes' Theorem?

Back

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

Front

If P(A) = 1/4 and P(B) = 1/2, what is P(A or B) if A and B are mutually exclusive?

Back

P(A or B) = P(A) + P(B) = 1/4 + 1/2 = 3/4.

Front

What is the difference between dependent and independent events?

Back

Dependent events are events where the outcome of one affects the other, while independent events do not influence each other.