Suppose that 40% of the students on a campus, who are

QUESTION:

Suppose that 40% of the students on a campus, who are married to students on the same campus, are female. Moreover, suppose that 30% of those who are married, but not to students at this campus, are also female. If one-third of the married students on this campus are married to other students on this campus, what is the probability that a randomly selected married student from this campus is a woman? Hint: Let M, C, and F denote the events that the random student is married, is married to a student on the same campus, and is female. For any event A, let Q(A) = P (A | M). Then, by Theorem 3.1, Q satisfies the same axioms that probabilities satisfy. Applying Theorem 3.3 to Q and, using the result of Exercise 15, we obtain P (F | M) = P (F | MC)P (C | M) + P (F | MCc )P (Cc | M).