Answer:
So, the probability is P=0.2383.
Explanation:
We know that recent statistics show that 62% of people wash their hands after using the restroom.
We get that p=0.62 and q=1-0.62=0.38.
If you shake hands with three random people, so n=3.
We calculate the probability that all of them washed their hands after previously using the restroom, so k=3.
We use the formula:

we get

So, the probability is P=0.2383.