3 The student body of a local college draws 40 of its studen

3. The student body of a local college draws 40% of its students from Ontario, 35% from the rest of Canada, and the remainder from outside Canada. Of those from Ontario, 60% are female, of those from the rest of Canada 25% are female, and of those from outside Canada, 15% are female.

a. What is the probability of a male student from Ontario?

b. What is the probability of a female student?

c. What is the probability of a male student who did not come from Ontario?

Solution

Let

M = male
f = female
O = ontario
C = canada
C\' = outside canada

A)

P(M n O) = P(O) P(M|O)

= 0.40*(1-0.60)

= 0.16 [ANSWER]

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b)

P(F) = P(O) P(F|O) + P(C) P(F|C) + P(C\') P(F|C\')

= 0.40*0.60 + 0.35*0.25 + 0.25*0.15

= 0.365 [ANSWER]
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c)

P(M n O\') = P(C) P(M|C) + P(C\') P(M|C\')

= 0.35*(1-0.25) + 0.25*(1-0.15)

= 0.475 [ANSWER]