On graduation day at a large university, one graduate is selected at random. Let A represent the event that the student is an engineering major, and let B represent the event that the student took a calculus course in college. Which probability is greater, P(A|B) or P(B|A)? Explain.
What will be an ideal response?
Given that a student is an engineering major, it is almost certain that the student took a calculus course. Therefore P(B|A) is close to 1. Given that a student took a calculus course, it is much less certain that the student is an engineering major, since many non-engineering majors take calculus. Therefore P(A|B) is much less than 1, so P(B|A) > P(A|B).
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