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?

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MrRoyal MrRoyal · Answer 1 · 2021-01-18T02:52:46+01:00

Answer:

[tex]Probability = 0.2975[/tex]

Step-by-step explanation:

Giving:

Swimming

[tex]P(Win[Swim])= 65\%[/tex]

Running

[tex]P(Win[Run])= 85\%[/tex]

Required

Determine the probability of winning at running and losing at swimming

First, we calculate the probability of losing at swimming using

[tex]P(Win) + P(Lose) = 1[/tex]

Substitute 65% for P(Win)

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

Collect Like Terms

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

[tex]P(Lose[Swim]) = 35\%[/tex]

The required probability is then calculated using:

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

[tex]Probability = 85\% * 35\%[/tex]

Convert to decimal

[tex]Probability = 0.85 * 0.35[/tex]

[tex]Probability = 0.2975[/tex]