Answer:
The probability that at least 1 of the 3 children is a boy is 0.875.
Step-by-step explanation:
The probability of a baby born being a girl or a boy is same, i.e.
P (G) = P (B) = 0.50.
A couple has 3 children.
Let X = number of boys.
The random variable X follows a Binomial distribution. The probability of a Binomial distribution is computed using the formula:
[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0, 1, 2...[/tex]
Compute the probability that at least 1 of the 3 children is a boy as follows:
P (At least 1 boy) = 1 - P (No boys)
P (X ≥ 1) = 1 - P (X = 0)
[tex]=1-{3\choose 0}(0.50)^{0}(1-0.50)^{3-0}\\=1-(1\times1\times0.125)\\=1-0.125\\=0.875[/tex]
Thus, the probability that at least 1 of the 3 children is a boy is 0.875.
