Men have a reputation for not wanting to ask for directions. A Harris study conducted for Lincoln Mercury indicated that 42% of men and 61% of women would stop and ask for directions. The U.S. Census Bureau's 2012 population estimate was that for individuals 18 or over, 48.2% were men and 51.8% were women. This exercise addresses this age group. Given that a driver stops to ask for directions, determine the probability that the driver was a man.
A) 0.518
B) 0.420
C) 0.316
D) 0.390

Question

Quizplus · Accepted Answer

To find the probability that a driver who stops to ask for directions is a man, we use Bayes' theorem or a basic probability approach. The probability that a driver is a man and stops to ask for directions is the product of the probability that a driver is a man (0.482) and the probability that a man would stop to ask for directions (0.42). This gives us 0.482 * 0.42 = 0.20244. The probability that a driver is a woman and stops to ask for directions is the product of the probability that a driver is a woman (0.518) and the probability that a woman would stop to ask for directions (0.61), which gives us 0.518 * 0.61 = 0.31598. The total probability that a driver stops to ask for directions is the sum of these two probabilities, 0.20244 + 0.31598 = 0.51842. Therefore, the probability that the driver was a man, given that the driver stops to ask for directions, is 0.20244 / 0.51842 ≈ 0.390.

Men Have a Reputation for Not Wanting to Ask for Directions