Most Americans, 75% 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 67% of the time and men wash only 46% of the time. Of the adults using the public restroom at a large grocery chain store, 59% are women. What is the probability that the next person to enter the restroom in this store washes his or her hands? (Enter your answer to two decimal places.)

To find the probability that the next person to enter the restroom in the store washes their hands, we can use conditional probability.

Let's break down the problem step by step:

Step 1: Find the probability that a person is a man or a woman.
Given information:
- Percentage of women using the restroom at the grocery chain store: 59%
- Percentage of men using the restroom at the grocery chain store: 100% - 59% = 41%
So the probability that the next person is a woman is 59% (or 0.59), and the probability that the next person is a man is 41% (or 0.41).

Step 2: Find the probability that a person washes their hands based on their gender.
Given information:
- Percentage of women who wash their hands: 67%
- Percentage of men who wash their hands: 46%
So the probability that a woman washes her hands is 67% (or 0.67), and the probability that a man washes his hands is 46% (or 0.46).

Step 3: Find the overall probability.
Since we want to find the probability that the next person entering the restroom washes their hands regardless of their gender, we need to consider the probabilities of both men and women while taking into account their proportions.

Probability = (Probability of being a woman * Probability of washing hands as a woman)
+ (Probability of being a man * Probability of washing hands as a man)

= (0.59 * 0.67) + (0.41 * 0.46)

= 0.3953 + 0.1886

= 0.5839

Therefore, the probability that the next person to enter the restroom in this store washes their hands is approximately 0.58 or 58%.

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