Events: 1 ≤ n ≤ 100 A=x is a perfect square, i.e. x=n^2 B=x is odd, i.e. n is odd P(A|B) =P(A∩B)/P(B) by definition of conditional probability (reads Probability that the number is a perfect square given that it is odd)
Since there are 10 perfect squares between 1 to 100 (1,4,9,16,25,36,49,64,81,100), out of which 5 are odd {1,9,25,49,81) So P(A∩B)=5/100 P(B)=probability of odd x {1,3,5,7,.....95,97,99} = 50/100=1/2 Therefore P(A|B)=(5/100)/(1/2)=1/10
