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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
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
.
- Equally as likely to be a boy or a girl, hence
.
The probability of one of each is P(X = 1), hence:
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