A family has two children. When asked if he has at least one daughter named Ann, the fatherreplies, "Yes." What is the probability that both children are girls, if we know that the family has at least one daughter named Ann?

33.3% probability that both children are girls, if we know that the family has at least one daughter named Ann.

Step-by-step explanation:

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

The family has two children.

The sample space, that is, the genders of the children may be divided in the following way, in which b means boy and g means girl.

b - b

b - g

g - b

g - g

We know that they have at least one girl. So the sample space is:

b - g

g - b

g - g

What is the probability that both children are girls, if we know that the family has at least one daughter named Ann?

Desired outcomes:

Both children being girls, so

g - g

1 desired outcome

Total outcomes

b - g

g - b

g - g

3 total outcomes

Probability

1/3 = 0.333

33.3% probability that both children are girls, if we know that the family has at least one daughter named Ann.