Question

in a certain country, the true probability of a baby being a girl is 0.476. among the next seven randomly selected births in the country, what is the probability that at least one of them is a boy?
the probability is
(round to three decimal places as needed.)

Explanation:

Step1: Find the probability of all being girls

The probability of a baby being a girl \(p = 0.476\). For \(n=7\) independent births, the probability that all are girls is \((0.476)^7\).

Step2: Use the complement rule

The probability that at least one is a boy is \(P(X\geq1)=1 - P(X = 0)\) (where \(X\) is the number of girls). So \(P(X\geq1)=1-(0.476)^7\).
Calculate \((0.476)^7\approx0.006\). Then \(1 - 0.006=0.994\).

Answer:

\(0.994\)