Most Americans, 67% 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 66% of the time and men wash only 43% of the time. Of the adults using the public restroom at a large grocery chain store, 58% 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.)
Terrible response, did not understand anything
Use a probability tree:
Next person
male: 42% wash his hands: 43%
female: 58% wash her hands 66%
P(wash)=42%*43% + 58%*66%
=0.5634
To find the probability that the next person to enter the restroom washes his or her hands, we need to calculate the overall probability of handwashing considering both men and women.
Given:
- 67% of Americans say frequent handwashing is the best way to fend off the flu.
- Women wash their hands only 66% of the time.
- Men wash their hands only 43% of the time.
- 58% of the adults using the public restroom are women.
We can calculate the probability of handwashing using the following steps:
Step 1: Calculate the overall percentage of adults who wash their hands in public restrooms.
For women:
Percentage of women who wash their hands = 66%
Percentage of women in the public restroom = 58%
Probability of women washing their hands = (Percentage of women who wash their hands) * (Percentage of women in the public restroom)
= 66% * 58%
= 0.66 * 0.58
= 0.3828
For men:
Percentage of men who wash their hands = 43%
Percentage of men in the public restroom = 42% (100% - 58%)
Probability of men washing their hands = (Percentage of men who wash their hands) * (Percentage of men in the public restroom)
= 43% * 42%
= 0.43 * 0.42
= 0.1806
Overall probability of handwashing = Probability of women washing their hands + Probability of men washing their hands
= 0.3828 + 0.1806
= 0.5634
Step 2: Round the overall probability to two decimal places.
Overall probability of handwashing = 0.5634 (rounded to two decimal places)
Therefore, the probability that the next person to enter the restroom in this store washes his or her hands is 0.56 (rounded to two decimal places).
To find the probability that the next person to enter the restroom at the grocery chain store washes their hands, we can use conditional probability. Let's break down the given information:
- 67% of Americans say frequent handwashing is the best way to fend off the flu.
- Women wash their hands in public restrooms 66% of the time.
- Men wash their hands in public restrooms 43% of the time.
- 58% of the adults using the public restroom are women.
To find the probability, we will first calculate the probability that the next person entering the restroom is a man or a woman. Then we will use this probability along with the gender-specific handwashing rates to calculate the overall probability.
First, let's find the probability that the next person entering the restroom is a woman:
Probability of a woman entering = 58% = 0.58
Next, let's find the probability that the next person entering the restroom is a man:
Probability of a man entering = 100% - Probability of a woman entering = 100% - 58% = 42% = 0.42
Now, let's calculate the overall probability of someone washing their hands, considering the gender-specific handwashing rates:
Probability of a woman washing her hands = 66% = 0.66
Probability of a man washing his hands = 43% = 0.43
Using these values, we can calculate the overall probability:
Overall probability = (Probability of a woman entering x Probability of a woman washing her hands) + (Probability of a man entering x Probability of a man washing his hands)
= (0.58 x 0.66) + (0.42 x 0.43)
= 0.3828 + 0.1806
= 0.5634
Therefore, the probability that the next person to enter the restroom washes his or her hands is approximately 0.56 (rounded to two decimal places).