Question

The probability that the mayor of Pawnee will run in another election is 2/3 . If they choose not to run in the election, then their deputy mayor will run in their place. The polls estimate that the current mayor has about a 60 % chance of winning the election, and if the deputy mayor runs they have about a 40 % chance of winning. Using this information, what is the probability that after this election that both the mayor and deputy mayor would lose?

Answer 1

To find the probability that both the mayor and deputy mayor would lose, we calculate the probabilities of each scenario separately and then multiply them. The probability is 0.16 or 16%.

Step-by-step explanation:

To find the probability that both the mayor and deputy mayor would lose, we need to consider two scenarios:

1. The mayor runs in the election and loses.
2. The mayor chooses not to run, and the deputy mayor runs in their place and loses.

In the first scenario, the probability that the mayor loses is 1 - 0.6 = 0.4. In the second scenario, the probability that the deputy mayor loses is 0.4.

Since these two scenarios are mutually exclusive, we can find the probability that both events occur by multiplying their individual probabilities: 0.4 * 0.4 = 0.16.

Therefore, the probability that both the mayor and deputy mayor would lose is 0.16, or 16%.