Question

Most Americans, 66% in fact, say frequent handwashing is the best way to fend off the flu. Despite that, when using public restrooms, women wash their hands only 63% of the time and men wash only 46% of the time. Of the adults using the public restroom at a large grocery chain store, 57% are women. What is the probability that the next person to enter the restroom in this store washes his or her hands?

Answer 1

The probability that the next person to enter the restroom washes their hands is approximately 55.69%, calculated using the given probabilities of men and women washing hands and the percentage of women who use the restroom.

Step-by-step explanation:

To calculate the probability that the next person to enter the restroom washes his or her hands, we consider the probabilities of women washing their hands (63%) and men washing their hands (46%) and the proportion of restroom users who are women (57%). We use these to find the overall probability of handwashing.

The probability P that a person washes their hands is given by:

P = P(Woman and washes hands) + P(Man and washes hands)

Since 57% of the restroom users are women, the other 43% are men. This leads to:

P = (57% × 63%) + (43% × 46%)

P = (0.57 × 0.63) + (0.43 × 0.46)

P = 0.3591 + 0.1978

P = 0.5569 or about 55.69%

Therefore, the probability that the next person to enter the restroom is likely to wash his or her hands is approximately 55.69%.