In a certain country, the true probability of a baby being a girl is 0.462. Among the next seven randomly selected births in the country, what is the probability that at least one of them is a boy ?

0.9956

Step-by-step explanation:

A baby is born either a boy or a girl. Thus, the probability that a boy is born PLUS the probability that a girl is born is 1.00.

Thus, the probability of a boy being born is 1.00-0.462, or 0.538.

Due to the either-or nature of this boy-or-girl phenomenon, binomial probability is called for. Here the number of trials, n, is 7; the probability of "success" (that is, the probability that a boy will be born) is 0.538. If we find the probability of 0 boys being born and subtract that from 1.00, we'll have the probability that at least one of the newborns is a boy.

Many of today's handheld calculators have probability distribution tools. We'll use binompdf (n, p, x) here, with n = 7, p = 0.538 and x = 0.

binompdf (7, 0.538, 0) = 0.0045. This represents that probability that no boy (s) is (are) born.

Then the prob. that at least one boy is born is 1.0000 - 0.0045, or 0.9956.