Question

The probability that the mayor of Mathville will stand for another election is . If she doesn't choose to run then her deputy will definitely run in the election, however if the mayor does run in the election her deputy mayor will not run against her. The probability that the mayor would be reelected if she ran is . If the deputy runs, he will win with probabilty. What is the probability that neither the mayor nor the deputy is elected? A.⁹/₄₀ B.³/₅ C.¹³/₈ D.⁷/₄₀ E.³¹/₄₀

Answer 1

The probability that neither the mayor nor the deputy is elected is 0.096.

Step-by-step explanation:

The probability that neither the mayor nor the deputy is elected can be calculated by multiplying the probabilities of three events:

1. The mayor stands for election and is not reelected, which has a probability of 1 - 0.6 = 0.4
2. The deputy stands for election and wins, which has a probability of 0.4
3. Neither the mayor nor the deputy stand for election, which has a probability of 1 - 0.4 = 0.6

To calculate the overall probability, multiply the three probabilities together: 0.4 * 0.4 * 0.6 = 0.096. Therefore, the probability that neither the mayor nor the deputy is elected is 0.096.

Answer 2

The probability that neither the mayor nor the deputy is elected is 0.02.

Step-by-step explanation:

In order to find the probability that neither the mayor nor the deputy is elected, we need to find the probability of two events happening:

1. The mayor doesn't run for the election
2. The deputy doesn't win if he runs

The probability that the mayor doesn't run for the election is (1 - probability of the mayor running) = (1 - 0.9) = 0.1

The probability that the deputy doesn't win if he runs is (1 - probability of the deputy winning) = (1 - 0.8) = 0.2

To find the probability of both events happening, we multiply the probabilities together: 0.1 * 0.2 = 0.02

So, the probability that neither the mayor nor the deputy is elected is 0.02.