Question

In a certain country, the true probability of a baby being a girl is 0.463. 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)

Answer 1

To find the probability that at least one of the next seven births is a boy, we can consider the complementary event. The probability of having no boys in all seven births is (0.537)^7. Therefore, the probability of having at least one boy in the next seven births is 1 - 0.051.

Step-by-step explanation:

To find the probability that at least one of the next seven births is a boy, we can consider the complementary event, which is the probability that none of the next seven births is a boy. The probability of having a girl in each birth is 0.463, so the probability of having a boy in each birth is 1 - 0.463 = 0.537.

Since each birth is independent, the probability of having no boys in all seven births is (0.537)^7 = 0.051. Therefore, the probability of having at least one boy in the next seven births is 1 - 0.051 = 0.949.