In an experiment of throwing three fair dice,the probability of getting a sum of $16$ is ..........

Let $N$ denote the sum of the numbers obtained when two dice are rolled. If the probability that $2^{N} < N!$ is $\frac{m}{n}$,where $m$ and $n$ are coprime,then $4m - 3n$ is equal to $......$.

$A$ man alternately tosses a coin and throws a dice,beginning with the coin. The probability that he gets a head in the coin before he gets a $5$ or $6$ in the dice is

$A$ die is formed so that the probability of getting a number $i$ when it is rolled is proportional to $i$ $(i=1, 2, 3, 4, 5, 6)$. The probability of getting an odd number on the die when it is rolled is

Three persons $P, Q$ and $R$ independently try to hit a target. If the probabilities of their hitting the target are $\frac{3}{4}, \frac{1}{2}$ and $\frac{5}{8}$ respectively,then the probability that the target is hit by $P$ or $Q$ but not by $R$ is

The probability that at least one of $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.3$,then $P(A') + P(B') = $