Question

melanie is running for mayor of her town and believes that the probability of her winning the election is 8/13. what is the probability of her losing the election? 1/13 5/13 8/13 13/8

Explanation:

Step1: Use probability formula

The probability of an event \(A\) and its complement \(\overline{A}\) satisfy \(P(A)+P(\overline{A}) = 1\). Let \(A\) be the event of Melanie winning the election, so \(P(A)=\frac{8}{13}\). Let \(\overline{A}\) be the event of Melanie losing the election.

Step2: Calculate the probability of losing

We know that \(P(\overline{A})=1 - P(A)\). Substitute \(P(A)=\frac{8}{13}\) into the formula: \(P(\overline{A})=1-\frac{8}{13}=\frac{13 - 8}{13}=\frac{5}{13}\).

Answer:

\(\frac{5}{13}\)