Two fair dice are rolled. The probability of the sum of digits on their faces being greater than or equal to $10$ is

Three coins are tossed once. Find the probability of getting $3$ heads.

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 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 $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A$ and $B$ are mutually exclusive.

Events $A, B$ and $C$ are mutually exclusive events such that $P(A)=\frac{3x+1}{3}$,$P(B)=\frac{1-x}{4}$ and $P(C)=\frac{1-2x}{2}$. The set of possible values of $x$ is in the interval

In each of the following experiments,specify the appropriate sample space: $A$ boy has a $1$ rupee coin,a $2$ rupee coin,and a $5$ rupee coin in his pocket. He takes out two coins out of his pocket,one after the other.