Question

The Smith family was one of the first to come to the U.S. They had 6 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Smith family had:

at least 5 girls

at most 3 girls

Answer 1

Let p , Probability of having a girl child be 0.5(given).

Now , n = 6 , p = 0.5

Using Binomial distribution,

P(x = a) =

A) P (atleast 5 girls) = P( x 5 )

= P(x =5) + P(x =6)

= +

= 6*0.015625 + 0.015625

= 0.09375 + 0.015625

= 0.109375

Thus, there is 0.109 (approx) Probability that there will be atleast 5 girls.

B) P(atmost 3 girls) = P(x 3) = 1 - P( x 4)

= 1 - P(x=4) - P(x = 5) - P(x =6)

= 1 - P(x =4) - 0.109375

= 1 - - 0.109375

= 1 - 15*0.015625 - 0.109375

= 1 - 0.234375 - 0.109375

= 0.65625

Thus, there is 0.656 (approx) Probability that there is atmost 3 girls out of 6.

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