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)
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