Respuesta :
Answer:
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:
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
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 [tex]P(B) = \frac{260}{435} = 0.5977[/tex]
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 [tex]P(A/B) = \frac{80}{260} = 0.3077[/tex]
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 [tex]P(A) = \frac{220}{435} = 0.5057[/tex]
Applying to the formula
[tex]P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.5977*0.3077}{0.5057} = 0.3637[/tex]
Given that a representative voted in favor of the bill, there is a 36.37% probability that he is a republican.
