Probability

Question

At a joint meeting, 100 Young Republicans and 75 Young Democrats are present to debate issues in the upcoming campus elections. On the issue of campus parking, 35% of the Young Democrats and 60% of the Young Republicans favor turning a campus green space into a parking lot. A campus newspaper reporter randomly selects a person from the group and finds that the person favors the parking space. Find the probability that the person selected is a Young Democrat. (Round your answer to three decimal places.)

Answer 1

There are 0.35(75) = 26.25 Young Democrats who favor the parking lot and 0.6(100) = 60 Young Republicans who favor the parking lot. That's a total of 26.25 + 60 = 86.25 parking-lot favorers.

 

Given that the newspaper has picked one of these 86.25 favorers, 26.25 of which are Young Democrats, the probability that the person selected is a Young Democrat is:

 

P(D) = (Young Democrat parking-lot favorers) / (total favorers)

P(D) = 26.25/86.25

P(D) = 0.304