The following data from a sample of 100 families show the record of college atte

Question

The following data from a sample of 100 families show the record of college attendance by fathers and their oldest sons: in 22 families, both father and son attended college; in 31 families, neither father nor son attended college; in 12 families, the father attended college while the son did not; and, in 35 families, the son attended college while the father did not.

1. What is the probability a son attended college given that his father attended college?

2. What is the probability a son attended college given that his father did not attend college?

3. Is attending college by the son independent of whether his father attended college? (yes or no)

Explanation / Answer

Based on the given information we can deduce the following:

Pr[F] = .12 + .22 = .34
Pr[F'] = 1 - .34 = .66
Pr[S] = .35 + .22 = .57
Pr[S'] = 1 - .57 = .43

a) Pr[S | F] = Pr[S and F] / Pr[F] = .22/.34 ˜ .6471 b) Pr[S | F'] = Pr[S and F'] / Pr[F'] = .35 / .66 ˜ .5303 c) F and S are independent events if and only if Pr[F]*Pr[S] = Pr[F and S] We are given Pr[F and S] = .22 However, Pr[F]*Pr[S] = (.34)(.57) = .1938 which does not equal .22 Therefore, F and S are NOT independent events.

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