Question

Determine the probability of selecting a two-child family with one boy and one girl assuming boys and girls are equally likely

Answer 1

Using the binomial distribution, it is found that there is a 0.5 = 50% probability of selecting a two-child family with one boy and one girl.

For each child, there are only two possible outcomes, either it is a boy, or it is a girl. The probability of a child being a boy or being a girl is independent of any other child, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

• x is the number of successes.
• n is the number of trials.
• p is the probability of a success on a single trial.

In this problem:

• Two children, hence $n = 2$.
• Equally as likely to be a boy or a girl, hence $p = 0.5$.

The probability of one of each is P(X = 1), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{2,1}.(0.5)^{1}.(0.5)^{1} = 0.5$

0.5 = 50% probability of selecting a two-child family with one boy and one girl.

A similar problem is given at brainly.com/question/24863377