Anumber from 1-100 is randomly selected. what is the probability that it is a perfect square, given that it is an odd number?

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

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