Question

In terms of eye colors only nine percent of humans population has blue eyes. Find the probability that out of 42 Americans at least 2 have blue eyes. I used a binomial formula?

Answer 1

Given that nine percent of human population has blue eyes

So probability that a selcted person has blue eye = 9/100 = 0.09

So p = 0.09

This is a binomial distribution, so a person can have blue eyes or can not have blue eyes.

Probability that a selcted person doest not have blue eye = 1 - 0.09 = 0.91

So q = 0.91

Here given n = 42 Americans

Probability of x people having blue eyes out of n people = * px * qn-x

We need probability of atleast 2 americans having blue eyes out of total 42 Americans

P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + ....... P(X=41) + P(X=42) = 1

P(X=0) + P(X=1) + P(X2) = 1

P(X2) = 1 - P(X=0) - P(X=1)

P(X=0) = * 0.090 * 0.9142-0

=[ 42! / 0! (42-0)! ] * 1 * 0.9142

= 1 * 1 * 0.019043

= 0.019043

P(X=1) = * 0.091 * 0.9142-1

= [ 42! / 1! (42-1)! ] * 0.09 * 0.9141

  = 42 * 0.09 * 0.020927

= 0.079102

P(X2) = 1 - 0.019043 - 0.079102

= 0.901855

The probability that out of 42 Americans at least 2 have blue eyes is 0.901855