Question

Damien is competing in both swimming and running at a competition. After analyzing himself and his competitors, he knows that he has a 65% chance of winning at swimming and an 85% chance of winning at running. What is the probability that he will win the running event, but lose the swimming event?

Answer 1

`Probability = 0.2975`

Explanation:

Giving:

Swimming

`P(Win[Swim])= 65\%`

Running

`P(Win[Run])= 85\%`

Required

Determine the probability of winning at running and losing at swimming

First, we calculate the probability of losing at swimming using

`P(Win) + P(Lose) = 1`

Substitute 65% for P(Win)

`65\% + P(Lose[Swim]) = 1`

Collect Like Terms

`P(Lose[Swim]) = 1 - 65\%`

`P(Lose[Swim]) = 35\%`

The required probability is then calculated using:

`Probability = P(Win[Run]) * P(Lose[Swim])`

`Probability = 85\% * 35\%`

Convert to decimal

`Probability = 0.85 * 0.35`

`Probability = 0.2975`