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According to exit polls from the 2000 presidential election, the probability of a voter identifying as gay (including lesbians) was P(G) = 0.04. The probability of voting for Bush, given that a voter was gay, was P(B given G) = 0.25, and the probability of voting for Bush, given that a voter was not gay, was P(B given not G) = 0.50.

Find P(G intersection B)
Find P(G' intersection B) Find P(B), the overall probability of voting for Bush, keeping in mind that a voter was either gay and voted for Bush or not gay and voted for Bush.

Respuesta :

Answer:

P(G∩B)=0.01

P(G'∩B)=0.48

P(B)=0.49

Step-by-step explanation:

The given probabilities are

P(G)=0.04

P(B/G)=0.25

P(B/G')=0.5

P(G intersection B)=P(G∩B)=?

According to definition of conditional probability

P(B/G)=P(G∩B)/P(G)

So,

P(G∩B)=P(G)*P(B/G)

P(G∩B)=0.04*0.25

P(G∩B)=0.01

Thus, P(G intersection B)=P(G∩B)=0.01.

Now, P(G' intersection B)=P(G'∩B)=?

According to definition of conditional probability

P(B/G')=P(G'∩B)/P(G')

So,

P(G'∩B)=P(G')*P(B/G')

P(G')=1-P(G)=1-0.04=0.96

P(G'∩B)=0.96*0.5

P(G'∩B)=0.48

Thus, P(G' intersection B)=P(G'∩B)=0.48.

Now, P(B)=?

We know a voter is either gay and voted for Bush or not gay and voted for Bush so,

P(B)=P(G∩B)+P(G'∩B)

P(B)=0.01+0.48

P(B)=0.49

Thus, the overall probability of voting for Bush P(B)=0.49.

The solution to each of the given conditional probabilities are;

P(G ∩ B) = 0.01

P(G' ∩ B) = 0.48

P(B) = 0.49

What is the probability of the intersections?

We are given;

P(G) = 0.04

P(B/G) = 0.25

P(B/G')=0.5

A) We want to find P(G ∩ B)

From definition of conditional probability, we can say;

P(B/G) = P(G ∩ B)/P(G)

Thus;

P(G ∩ B) = P(G) * P(B/G)

P(G ∩ B) = 0.04 * 0.25

P(G ∩ B) = 0.01

B) We want to find P(G' ∩ B)

From conditional probability, we can say that;

P(B/G') = P(G' ∩ B)/P(G')

Thus;

P(G' ∩ B) = P(G') * P(B/G')

P(G') = 1 - P(G)

P(G') = 1 - 0.04

P(G') = 0.96

Thus;

P(G' ∩ B) = 0.96 * 0.5

P(G' ∩ B) = 0.48

C) We want to find P(B)

From the question, we can say that;

P(B) = P(G ∩ B) + P(G' ∩ B)

P(B) = 0.01 + 0.48

P(B) = 0.49

Read more about conditional probability at; https://brainly.com/question/23382435