Question

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

Answer 1

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.

Explanation:

Conditional Probability

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

`P(B|A) = (P(A \cap B))/(P(A))`

In which

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

`P(A \cap B)` 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

`P(A) = 0.43*0.36 + 0.55*0.64 = 0.5068`

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

55% of 64%. So

`P(A \cap B) = 0.55*0.64 = 0.352`

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

`P(B|A) = (P(A \cap B))/(P(A)) = (0.352)/(0.5068) = 0.6946`

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.