Question

In a certain country 12% of houses have solar heating. 19 houses are chosen at random. Find the probability that fewer than 4 houses have solar heating. the answer is in the picture ,the thing i don't understanding is from where did the brought 0.88 ?

Answer 1

This a binomial distribution of probability

Explanation:

For a binomial distribution `B(19,0.12)`

If `p=0.12` then `q=1-p=1-0.12=0.88`

Then
`P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=`

`=(0.88)^19+C_(1,19)(0.12)(0.88)^18+C_(2,19)(0.12)^2(0.88)^17+C_(3,19)(0.12)^3(0.88)^16=0.813`