Question

In a certain city, the true probability of a baby being a boy is 0.559. Among the next eight randomly selected births, find the probability that at least one of them is a boy. (round to three decimal places)

Answer 1

This is a direct application of Binomial distribution.

Let X be a number of baby boy among 8 births.

Here, X ~ Binomial (n = 8, p = 0.559)

We want to find, P(X ≥ 1)

P(X ≥ 1)

= 1 - P(X < 1)

= 1 - P(X = 0)

= 1 - [ ⁸C₀ * (0.559)⁰ * (1 - 0.559)^8-0 ]

= 1 - [ 1 * 1 * (0.441)⁸ ]

= 1 - 0.001

= 0.999

Therefore, the probability that at least one of them is a boy is 0.999