Question

What is conditional probability explain with an example?

Answer 1

conditional probability is the probability of an event ( A ), given that another event ( B ) has already occurred.

formula for conditional probability is given as

P(A/B) = P(A int. B)/P(B)

for example :-

A family has two children. what is the probability that both the children are boys given that at least of them is boy.

In the following example it has already given that in two one is boy so probability P(B) = 3/4 as 4 cases are possible and P(A) =1/4 because in only one case both boys are possible. Also int. stands for intersection of the events of the two sample spaces which in this case would be equal to 1/4 . Hence probability P(A/B)= 1/4 ÷ 3/4 = 1/3