Find the probability that when a couple has four children, at least one of them is a girl. (Assume that boys and girls are equally likely.) The probability is nothing that at least one of the four children is a girl.

The probability of an event is how likely the event is to happen. The probability that at least one of the 4 children is a girl is 0.9375.

Given that:

----- Because both have equal probabilities

This probability is an illustration of binomial probability where:

The probability that at least one of the 4 children is a girl is represented as:

Using complement rule:

---- i.e. 1 - the probability that none of the children is a girl

So, we have:

So, we have:

Hence, the probabilities that at least one of the 4 children is a girl is 0.9375.

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0.9375 = 93.75% probability that at least one of the four children is a girl.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We have the following sample space

In which b means boy, g means girl

b - b - b - b

b - b - b - g

b - b - g - b

b - b - g - g

b - g - b - b

b - g - b - g

b - g - g - b

b - g - g - g

g - b - b - b

g - b - b - g

g - b - g - b

g - b - g - g

g - g - b - b

g - g - b - g

g - g - g - b

g - g - g - g

Total outcomes

There are 16 total outcomes(size of the sample space)

Desired outcomes

Of these outcomes, only 1(b - b - b - b) there is not a girl.

So the number of desired outcomes is 15.

Probability:

0.9375 = 93.75% probability that at least one of the four children is a girl.