Question: High school rank. Select a first-year college student at random and ask what his or her academic rank was in high school. Here are the

High school rank. Select a first-year college student at random and ask what his or her academic rank was in high school. Here are the probabilities, based on proportions from a large sample survey of first-year students:

Rank: Top 20% Second 20% Third 20% Fourth 20% Lowest 20%

Probability: 0.41 0.23 0.29 0.06 0.01

(a) Choose two first-year college students at random. Why is it reasonable to assume that their high school ranks are independent?

(b) What is the probability that both were in the top 20% of their high school classes?

(c) What is the probability that the first was in the top 20% and the second was in the lowest 20%?

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