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According to exit polling from the 2014 U.S. midterm elections, 36% of voters had a household income less than $50,000, while 64% had a household income of at least $50,000. Forty-three percent of voters from house-holds making less than $50,000 voted for the Republican party in the election, while 55% percent of voters from households making at least $50,000 voted Republican. What is the probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000

Sagot :

Answer:

0.6946 = 69.46% probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Republican

Event B: From a household that makes at least $50,000.

Probability of Republican:

43% of 36%(makes less than $50,000).

55% of 64%(makes more than $50,000).

So

[tex]P(A) = 0.43*0.36 + 0.55*0.64 = 0.5068[/tex]

Republican and from a household that makes at least $50,000.

55% of 64%. So

[tex]P(A \cap B) = 0.55*0.64 = 0.352[/tex]

What is the probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.352}{0.5068} = 0.6946[/tex]

0.6946 = 69.46% probability that a randomly selected Republican voter from the exit poll is from a household that makes at least $50,000.

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