Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

The chance of getting a doublet with $2$ dice is

The probabilities of $A, B,$ and $C$ solving a problem are $\frac{1}{3}, \frac{2}{7},$ and $\frac{3}{8}$ respectively. If all three try to solve the problem simultaneously,the probability that exactly one of them will solve it is:

From a well-shuffled pack of cards,one card is drawn at random. The probability that the card drawn is an ace is

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$. Then,the probability that both of them occur together is:

Two coins (a one rupee coin and a two rupee coin) are tossed once. Find the sample space.