Question

In one town, 77% of adults have health insurance. What is the probability that 5 adults selected at random from the town all have health insurance? Round to the nearest ten- thousandth if necessary.

Answer 1

Let , X be the number of adult who have health insurance.

Here ,

Where, n=5 , p=0.77 , q=1-p=0.23

The pmf of X is ,

; x=0,1,2,......,n

= 0 ; otherwise

Now , we want to find the P(X=5)

Therefore ,

Therefore , the probability that 5 adults selected at random from the town all have health insurance is 0.2707.