Binomial Probablity

Question

The Jones family was one of the first to come to the U.S. They had 7 children. Assuming that the probability of a child being a girl is .5, find the probability that the Jones family had:

at least 4 girls?

at most 2 girls?

Answer 1

At least 4 is .5; note that no calculations are needed for this, since the probability of a female is .5; you are equally likely to have 4 or more girls and 4 or more boys, and you must have 4 or more of 1 or the other.

Alternatively, in Excel,1 - binomdist(3,7,.5,1) = .5

At most 2 is (C(7,0)+C(7,1)+C(7,2))/2^7 = (1+7+21)/128 = 29/128 = .2265625

Alternatively, in Excel, binomdist(2,7,.5,1) = .2265625