4.25 High school rank. Select a first-year college student at random and ask wha

Question

4.25 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% 0.23 Fourth 20% 0.06 Third 20% Lowest 20% Probability 0.41 0.29 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%?

Explanation / Answer

(a)

Each student is independent from other and also they may come from different schools so it is reasonable to assume that their high school ranks are independent.

(b)

Since students are independent from each other so the probability that both were in the top 20% of their high school classes is

P(both were in top 20%) =P(top 20%)P(top 20%) = 0.41 *0.41 = 0.1681

(c)

Since students are independent from each other so the probability that the first was in the top 20% and the second was in the lowest 20% is

P(the first was in the top 20% and the second was in the lowest 20%) =P(top 20%)P(lowest 20%) = 0.41 *0.01 = 0.0041

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