Question

The Wilson family was one of the first to come to the U.S. They had 4 children. Assuming that the probability of a child being a girl is .5, find the probability that the Wilson family had: at least 3 girls? at most 3 girls?

Answer 1

Answer:

Total number of children = 4

Probability of a child being a girl = 0.5

Probability of child being a boy = 1 - 0.5 = 0.5

Probability that the Wilson family had atleast 3 girls?

P(X=3) + P(X=4) = ⁴C₃(0.5)^3*(0.5) + (0.5)^4

=4*0.0625 + 0.0625 = 0.3125

Probability that the Wilson family had atmost 3 girls?

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

(0.5)^4 + ⁴C₁*(0.5)^1*(0.5)^3 + ⁴C₂*(0.5)^2*(0.5)^2 + ⁴C₃*(0.5)^3*(0.5)^1

0.0625 + 4*0.0625 + 6*0.0625 + 4*0.0625 = 0.9375