Suppose that 5 percent of men and 025 percent of women are c

Suppose that 5 percent of men and 0.25 percent of women are colorblind. If a colorblind person is
chosen at random, what is the probability of that person being male (assuming that there are an equal number
of males and females)? What if the population had twice as many males as females?

Solution

a)

Let
M = male
F = female
C = color blind

Thus, as

P(C) = P(M) P(C|M) + P(F) P(C|F) = 0.50*0.05 + 0.50*0.0025 = 0.02625

Thus,

P(M|C) = P(M) P(C|M) / P(C) = 0.50*0.05/0.02625 = 0.952380952 [ANSWER]

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b)

If
P(M) = 0.6666667
P(F) = 0.3333333

Thus, as

P(C) = P(M) P(C|M) + P(F) P(C|F) = 0.6666667*0.05 + 0.3333333*0.0025 = 0.034166668

Thus,

P(M|C) = 0.666666667*0.05/0.034166668 = 0.975609719 [ANSWER]