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There are 5 juniors and 10 seniors (one of which is Amelia), trying to win a sch

ID: 3216967 • Letter: T

Question

There are 5 juniors and 10 seniors (one of which is Amelia), trying to win a scholarship to a summer music program. Only 3 students can win, and the winners will be selected randomly by pulling names out of a hat.

a) If students can win more than once and the students are independent from each other, what is the probability that the name-puller will call the first senior on the third name?

b) What is the probability that the first person to win a scholarship is a senior?

c) What is the probability that the third person to win a scholarship is a senior?

Explanation / Answer

P(junior) = 5/15 = 1/3

P(senior) = 2/3

a) P(first senior on third name) = P(first two are juniors and third is senior)

= (1/3) x (1/3) x (2/3) = 2/27

b) P(first person  to win a scholarship is a senior) = 2/3

c) P(the third person to win a scholarship is a senior) = 1x1x 2/3 = 2/3

(assuming the conditions are same as that of in part a)