If a couple plans to have 8 children, what is the probability that there will be at least one boy? Assume boys and girls are equally likely. Is that probability high enough for the couple to be very confident that they will get at least one boy in 8 children?The probability is ___ . ?(Type an integer or a simplified? fraction.

99.61% probability that there will be at least one boy, which is high enough for the couple to be very confident that they will get at least one boy in 8 children.

The probability is 0.9961

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they are a boy, or they are a girl. The probability of a children being a boy is independent from the probability of other children being a boy. 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.

Assume boys and girls are equally likely.

This means that

If a couple plans to have 8 children, what is the probability that there will be at least one boy?

This is when

We know that either there are no boys, or there is at least one boy. The sum of the probabilities of these events is decimal 1. So

In which

Any probability above 95% is considered very high.

99.61% probability that there will be at least one boy, which is high enough for the couple to be very confident that they will get at least one boy in 8 children.