Question

"Find the indicated probability." Recent statistics show that 62% of people wash their hands after using the restroom. If you shake hands with three random people, what is the probability that all of them washed their hands after previously using the restroom

Answer 1

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:

`\boxed{P(X=k)=C_k^n\cdot p^k\cdot q^(n-k)}`

we get

`P(X=3)=C^3_3\cdot 0.62^3\cdot 0.38^(3-3)\\\\P(X=3)=1\cdot 0.2383 \cdot 1\\\\P(X=3)=0.2383`

So, the probability is P=0.2383.