. Assume that each born child is equally likely


to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that :

(i) the youngest is a girl.

(ii) at least one is a girl.

 

Best Answer

Explanation:

Conditional probability is the measure of the likelihood of an event B occurring, given that event A has occurred previously.

It can be calculated by dividing the probability of the intersection of A and B by the probability of A.

dividing the probability

A family has two children.

Let girl children be denoted by g and the boy children be denoted by b.

(i) To find the probability that both the children are girls, given that the youngest is a girl.

Let event A: the youngest child is a girl, and

Event B both the children 

dividing the probability

Hence, the probability that both the children are girls, given that the youngest is a girl is 1/2

(ii) To find the probability that the children are girls, given that at least one is a girl.

Thus, we have sample space: {(g,g),(g,b),(b,g) }and EnF = {(g,g)}.

Let event E: both the children are girls, and

Event :F  at least one child is a girl

dividing the probability

Hence, the probability that the children are girls, given that at least one is a girl is 1/3

Final Answer:

(i) The probability that both the children are girls, given that the youngest is a girl is 1/2

(ii) The probability that the children are girls, given that at least one is a girl is1/3 

 

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