Answer: (C) \(\frac{2}{3}\)
Let S be the sample space of rolling a dice.
Then, S = {1, 2, 3, 4, 5, 6} ⇒ n(S) = 6
Let A: Event of rolling an odd number and
B: Event of rolling a prime number.
Then, A = {1, 3, 5} ⇒ n(A) = 3
B = {2, 3, 5} ⇒ n(B) = 3
A ∩ B = {3, 5} ⇒ n(A ∩ B) = 2
∴ P(A) =\(\frac{3}{6} =\frac{1}{2}\) ,P(B) =\(\frac{3}{6} =\frac{1}{2}\) , \(P(A\,\cap\,B)=\frac{2}{6}=\frac{1}{3}\)
Now, P(Rolling a prime number, if the outcome is an odd number)
\(=P\big(\frac{B}{A}\big) = \frac{P(A\,\cap\,B)}{P(A)}= \frac{1/3}{1/2} \)
\(=\frac{2}{3}\)
