Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children: (a) What is the probability of getting one child of each sex?

49.97% probability of getting one child of each sex

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they are a boy, or they are a girl. The sex of a children is independent of other children, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The probability that a couple’s first child is a boy is 0.512.

This means that

The will have two children:

This means that

(a) What is the probability of getting one child of each sex?

This is P(X = 1).

49.97% probability of getting one child of each sex

3x^3-x^2+6x-9

21

step-by-step explanation:

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