There are 435 representatives in the house. suppose that 130 representatives are democrats and 260 are republicans; the rest are independents. assume that no representative belongs to more than one political party. a large infrastructure bill has barely been approved: 130 democrats, 80 republicans, and 10 independents voted in favor of the bill. given that a representative voted in favor of the bill, what is the probability that the representative is a republican? enter an answer that is correct to four decimal places.

Given that a representative voted in favor of the bill, there is a 36.37% probability that he is a republican.

Step-by-step explanation:

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula:

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

In your problem we have that:

What is the probability that the representative is a Republican, given that he voted in favor of the bill?

P(B) is the probability that the representative is a Republican. There are 435 representatives in the house, of which 260 are republicans. So

P(A/B) is the probability that the representative voted in favor of the bill, given that he is a Republican. There are 260 republicans, of which 80 voted in favor of the bill. So

P(A) is the probability that someone voted in favor of the bill. There are 435 representatives, and 130 + 80 + 10 = 220 voted in favor of the bill. So

Applying to the formula

Given that a representative voted in favor of the bill, there is a 36.37% probability that he is a republican.

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