In a single throw of two dice,the probability of obtaining a total of $7$ or $9$ is:

Three students $A$,$B$ and $C$ are running a race. $A$ and $B$ have the same probability of winning and each is twice as likely to win as $C$. Then,the probability that $B$ or $C$ wins is equal to (assuming there are no ties)

Two players play the following game: $A$ writes $3, 5, 6$ on three different cards; $B$ writes $8, 9, 10$ on three different cards. Both draw randomly two cards from their collections. Then,$A$ computes the product of the two numbers he/she has drawn,and $B$ computes the sum of the two numbers he/she has drawn. The player getting the larger number wins. What is the probability that $A$ wins?

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the events $A$ and $B$.

The probability of getting a sum of $9$ when two dice are thrown is

Let $A$ and $B$ be two independent events. The probability that both $A$ and $B$ happen is $\frac{1}{12}$ and the probability that neither $A$ nor $B$ happens is $\frac{1}{2}$. Then