a What is the probability that the student is both a sophomo

(a) What is the probability that the student is both a sophomore and a physics major?

(b) Given that the student selected is a physics major, what is the probability that she is also a sophomore?

Write your responses as fractions.

Solution

Note that

N = N(P) + N(S) - N(P and S) + N(neither)

Thus,

39 = 21 + 20 - N(P and S) + 8

Thus,

N(P and S) = 10

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Thus,

P(P and S) = 10/39 [answer, a]

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P(S|P) = N(P and S) / N(P)

= 10/21 [answer, b]