Questions: In a certain country, the true probability of a baby being a girl is 0.479. 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.)

Solution Steps

We are tasked with finding the probability that at least one of the next seven randomly selected births in a certain country is a boy, given that the probability of a baby being a girl is \( p = 0.479 \). Consequently, the probability of a baby being a boy is \( q = 1 - p = 0.521 \).

To find the probability of having at least one boy, we first calculate the probability of having all girls in the seven births. This can be expressed using the binomial probability formula:

\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \]

For our case, where \( n = 7 \) and \( x = 0 \) (indicating all births are girls), the formula simplifies to:

\[ P(X = 0) = \binom{7}{0} \cdot (0.479)^0 \cdot (0.521)^7 \]

Calculating this gives:

\[ P(X = 0) = 1 \cdot 1 \cdot (0.521)^7 \approx 0.010 \]

The probability of having at least one boy is the complement of the probability of having all girls:

\[ P(\text{at least one boy}) = 1 - P(X = 0) \]

Substituting the value we calculated:

\[ P(\text{at least one boy}) = 1 - 0.010 = 0.990 \]

Final Answer