Question

A family plans to have 3 children. For each birth, assume that the probability of a boy is the same as the probability of a girl. What is the probability that they will have at least one boy and at least one girl?

a. 0.5
b. 0.125
c. 0.75
d. 0.875
e. None of these

Answer 1

c. 0.75

Explanation:

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

We have the following sample space

That is, the possible outcomes.

I am going to call boys b and girls g

b - b - b

b - b - g

b - g - b

b - g - g

g - b - b

g - b - g

g - g - b

g - g - g

Total outcomes:

8 outcomes

What is the probability that they will have at least one boy and at least one girl?

Desired outcomes:

At least one boy and at least one girl

b - b - g

b - g - b

b - g - g

g - b - b

g - b - g

g - g - b

Six desired outcomes.

Probability

`P = (6)/(8) = 0.75`

The correct answer is:

c. 0.75