## Problem 1166

If the probability is 0.81 that a candidate wins the election, what is the probability that he loss?

**Solution:-**

Suppose that we divide a final sample space into two sunset E and E’ such that E∩E’ = ø, that is they are mutually exclusive, and EUE’ = S. Then E’ called the complement of E relative to S. Thus, E’ contains all the elements of S that are not in E.

Because the events are mutually exclusive, P(E’) = 1- P(E).

Let E = the candidate wins and let E’ = the candidate, use P(E’) = 1 –P(E) to find the probability that the candidate loses the election.

Substitute P(E) into the equation below.

P(E’) = 1-0.81

Calculate P(E’)

P(E’) = 0.19

Therefore, the probability that the candidate loses the election is 0.19.