Twenty percent of the contestants in a scholarship competition come from Pylesville High School, 40% come...

Twenty percent of the contestants in a scholarship competition come from Pylesville High School, 40% come from Millerville High School, and the remaining come from Lakeside High School. Two percent of the Pylesville students are among the scholarship winners; 3% of the Millerville contestants and 5% of the Lakeside contestants win. a) If a winner is chosen at random, what is the probability that they are from Lakeside? b) What percentage of the winners are from Pylesville?

Solutions

Expert Solution

P : Event of contestant come from Pylesville High School

P(P) = 20/100 =0.2

M : Event of contestant come from Millerville High School

P(M) = 0.40

L : Event of contestant come from Millerville High School

P(L) = 1-0.2-0.4 = 0.4

W : Event of chosen contestant is a winner

Given,

Two percent of the Pylesville students are among the scholarship winners : P(W|P) = 2/100 =0.02

3% of the Millerville contestants : P(W|M) = 3/100 =0.03

5% of the Lakeside contestants win:P(W|L) = 5/100 =0.05

a) If a winner is chosen at random, probability that they are from Lakeside = P(L|W)

By Bayes theorem,

If a winner is chosen at random, what is the probability that they are from Lakeside = P(L|W) =0.5556

b) percentage of the winners are from Pylesville = P(P|W)*100

Percentage of the winners are from Pylesville = P(P|W)*100 =0.1111*100 =11.11%

milcah answered 2 hours ago

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