Question

A die is rolled. If the outcome is an odd number, what is the probability that it is prime?

Answer 1

Consider the given events.
A = The number is odd
B = The number is prime

Clearly,
A = {1, 3, 5}
B = {2, 3,5}

$$\begin{gathered} \mathrm{Now}, \\ A\cap B=\left\{3,5\right\} \\ \therefore \mathrm{Required}\mathrm{probability}=P\left(B/A\right)=\frac{n\left(A\cap B\right)}{n\left(A\right)}=\frac{2}{3} \end{gathered}$$