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

Step-by-step 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.