Question

Fifteen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle at most 8 cases of the disease. What is the probability that the hospital’s capacity will be exceeded?a. .146

b. .905
c. .787
d. .854
e. .0950

Answer 1

Answer: e. .0950

Explanation:

Let X be the number of people that can be cure from disease.

Since each people independently has a 40% chance of contracting the disease.

So ,
`X\sim Binomial(n=15,p=0.40)`

A hospital has the capacity to handle at most 8 cases of the disease.

Binomial distribution formula :
`P(X=x)= ^nC_xp^x(1-p)^(n-x)`

Then , the probability that the hospital’s capacity will be exceeded

`P(X>8)=1-P(X\leq8)\\\\=1-0.905\ \ [\text{Using Binomial distribution table for n=15 , x=8 and p=0.4.}]`

`=0.095`

Hence, the probability that the hospital’s capacity will be exceeded is e. .0950.

Thus , the correct option is e. .0950.