Question

Suppose John and his wife know that the probability of one of their children having blue eyes is 20%. If John and his wife have 5 children, what is the probability that less than 3 children will have blue eyes?  

Round your answer to 4 decimal places.

Answer 1

Given that ,

p = 0.20

1 - p = 1 - 0.20= 0.80

n = 5

Using binomial probability formula ,

P(X = x) = (n C x) * px * (1 - p)n - x

P(X <3 ) = P(X=0) +P(X=1)+P(X=2)

= (5 C 0) *0.200 * (0.80)2+(5 C 1) *0.201 * (0.80)4+(5 C 2) *0.202 * (0.80)3

probability =0.9421