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 mathematics major?

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

Write your responses as fractions.

Solution

Note that

N(tot) = N(sop) + N(mat) - N(mat and sop) + N(not mat nor sop)

Thus,

65 = 28 + 38 - N(mat or sop) + 5

N(mat and sop) = 6

Thus,

P(mat and sop) = N(mat and sop)/N(tot) = 6/65 [ANSWER, A]

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P(mat|sop) = P(mat and sop)/P(sop)

or

P(mat|sop) = N(mat and sop)/N(sop)

= 6 / 28

=3/14 [ANSWER, B]