Question

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.

Answer 1

Answer:

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:

$P = \frac{15}{16} = 0.9375$

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