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The American Society of Microbiology periodically estimates the percentage of pe

ID: 3369429 • Letter: T

Question

The American Society of Microbiology periodically estimates the percentage of people who wash their hands after using a public restroom. (Yes, these scientists spy on people in public restrooms, but it's for a good cause.) The Society reports that about 60% of men and 80% of women wash their hands after using a public restroom. Suppose you observe one man and one woman at random. Compute each of these probabilities.

Round each answer to three decimal places.

a. P(both the man and the woman wash their hands) =

d. P(man washes his hands | woman washes her hands) =

Explanation / Answer

a) P(both the man and the woman wash their hands) = 0.6 * 0.8 = 0.480

b) P(neither wash his or hands) = 0.4 * 0.2 = 0.080

c) P(at least one washes his or handes) = 0.6 * 0.2 + 0.8 * 0.4 + 0.6 * 0.8 = 0.920

d) P(man washes his hands | woman washes her hands) = P(man washes his hands and woman washes her hands)/P(woman washes her hands) =  0.6 * 0.8/0.8 = 0.600