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

Answer:

$Probability = 0.2975$

Step-by-step 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

$Probability = 0.85 * 0.35$

$Probability = 0.2975$