Question

In a presidential race, there is a 59% chance that the Republican candidate will win. A Republican judge is hoping to be appointed to a federal position. The judge believes that if the Republican candidate wins the presidency, she will have a 86% chance of being appointed to a federal position. If the Republican candidate does not win the presidency, she believes that she only has a 31% chance of being appointed to a federal position.

Let R = the Republican candidate wins the presidential race and F = the judge is appointed to a federal position

(Round all answers to four decimal places.)

Use a probability tree to answer the following questions:

a) What is the probability that the judge will be appointed to a federal position?

b) What is the probability that the judge will be appointed to a federal position and the Republican presidential candidate will win?

c) What is the probability that the Republican presidential candidate will lose and the judge will not be appointed to a federal position?

Answer 1

P(R) = 0.59

P(F | R) = 0.86

P(F | R') = 0.31

a) P(F) = P(F | R) * P(R) + P(F | R') * P(R')

            = 0.86 * 0.59 + 0.31 * (1 - 0.59)

            = 0.6345

b) P(F and R) = P(F | R) * P(R) = 0.86 * 0.59 = 0.5074

c) P(F') = 1 - P(F) = 1 - 0.6345 = 0.3655

P(F' | R') = 1 - P(F | R') = 1 - 0.31 = 0.69

P(F' and R') = P(F' | R') * P(R') = 0.69 * (1 - 0.59) = 0.2829