Answer:
So, the probability is P=0.2383.
Step-by-step 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:
[tex]\boxed{P(X=k)=C_k^n\cdot p^k\cdot q^{n-k}}[/tex]
we get
[tex]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[/tex]
So, the probability is P=0.2383.
