From the set of all families with two children a a family is

From the set of all families with two children,

(a) a family is selected at random and is found to have a girl. What is the probability that the other child of the family is a girl?

(b) a child is selected at random and is found to be a girl. What is the probability that the other child of this girl\'s family is also a girl?

Solution

Since probability of a boy or girl is same, that is 0.5.

a) The required probability is given by using conditional probability

That is Required Prob. = Prob. both are girls/ Prob. first is girl =(1/4)/(1/2)=0.5

If the number of families were given, the above probability would be different

b)

The required probability is given by using conditional probability

That is Required Prob. = Prob. both are girls/ Prob. first is girl =(1/4)/(1/2)=0.5