Conditional Probability

Front

What is Conditional Probability?

Back

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

Front

How is Conditional Probability calculated?

Back

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

Front

What does P(A|B) represent?

Back

The probability of event A occurring given that event B has occurred.

Front

What is the formula for Total Probability?

Back

P(A) = P(A|B)P(B) + P(A|¬B)P(¬B), where ¬B is the complement of B.

Front

If P(A|B) = 0.5 and P(B) = 0.4, what is P(A and B)?

Back

P(A and B) = P(A|B) * P(B) = 0.5 * 0.4 = 0.2.

Front

What is the Law of Total Probability?

Back

It states that the total probability of an event can be found by considering all possible ways that event can occur.

Front

What is the difference between independent and dependent events?

Back

Independent events do not affect each other's probabilities, while dependent events do.

Front

If two events A and B are independent, what is P(A and B)?

Back

P(A and B) = P(A) * P(B).

Front

What is Bayes' Theorem?

Back

A way to find a conditional probability when the reverse conditional probability is known: P(A|B) = [P(B|A) * P(A)] / P(B).

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.