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 denoted?

Back

P(A|B), which represents the probability of event A occurring given that event B has occurred.

Front

What is the formula for Conditional Probability?

Back

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

Front

What does P(Female|Part Time) represent?

Back

The probability that a student is female given that they are a part-time student.

Front

If P(A) = 0.6 and P(B) = 0.5, what is P(A and B) if A and B are independent?

Back

P(A and B) = P(A) * P(B) = 0.6 * 0.5 = 0.3.

Front

What is the relationship between P(A|B) and P(B|A)?

Back

They are related through Bayes' theorem: P(A|B) = [P(B|A) * P(A)] / P(B).

Front

What is the probability of passing given that a student studies?

Back

This is an example of conditional probability, denoted as P(Pass|Study).

Front

If the probability of event A is 0.4 and the probability of event B is 0.3, what is P(A|B) if A and B are dependent?

Back

P(A|B) cannot be determined without additional information about the relationship between A and B.

Front

What is the significance of the denominator in the conditional probability formula?

Back

The denominator, P(B), represents the total probability of the condition under which we are calculating the probability of A.

Front

What does it mean if P(A|B) = 0?

Back

It means that event A cannot occur if event B has occurred.