5. When the probability of event B is affected by he occurrence of event A, the

Question

5. When the probability of event B is affected by he occurrence of event A, the events are not independent. Let P(B | A) denote the probability of B given the condition that A has occurred. This is called a conditional probability.

Type I by holding down shift and type

For independent events A and B, P(B | A) = P(b), and P(A | B)= P(A)

For dependent events A and B

P(B | A) not equal P(B). The occurrence of A has changed the probability of B.

P(A | B) not equal P(A). The occurrence of B has changed the probability of A.

For dependent events, P(A and B) = P(A) x P(B | A) = P(B) x P(A | B). This is the General Multiplication Rule.

Assume the following joint and marginal probabilities:

In favor            Democrat            Republican           row total

Yes                       0.15                      0.20                     0.35

No                       0.25                       0.40                     0.65

Column

When we know the condition that some event has occurred, the table reduces to a row or column matching the condition. For example, when we know that the party is democrat, the table reduces to the democrat column:

In Favor            Democrat

Yes                       0.15

No                        0.25

Column total        0.40

P(Yes | Democrat) is the probability of event Yes given the condition that the event Democrat has occurred. In condition Democrat, yes occurs at a rate of 0.15 and 0.40. So P(Yes | Democrat) = 0.15/0.40 = 0.375.

P(male | republican) is a ___________ probability

Marginal

Conditional

joint

Explanation / Answer

P(Male | Republican) represents the probability of selecting a male given that he is a republican.

Hence,

It is a conditional probability.

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