If $A, B, C$ are three mutually exclusive and exhaustive events of an experiment such that $P(A)=2 P(B)=3 P(C)$,then $P(B)$ is equal to

If $A$ is a sure event,then the value of $P(\text{not } A)$ is:

The probability of solving a problem by three persons $A, B$ and $C$ independently is $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{3}$ respectively. Then the probability that the problem is solved by exactly two of them is

$A$ die has two faces each with number $1$,three faces each with number $2$,and one face with number $3$. If the die is rolled once,determine $P(2)$.

Let the sum of two positive integers be $24$. If the probability,that their product is not less than $\frac{3}{4}$ times their greatest positive product,is $\frac{m}{n}$,where $\operatorname{gcd}(m, n)=1$,then $n-m$ equals :

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