If $A$,$B$,and $C$ are mutually exclusive and exhaustive events of a sample space $S$ such that $P(B) = \frac{3}{2} P(A)$ and $P(C) = \frac{1}{2} P(B)$,then $P(A) = $

When a die is thrown twice,what is the probability of getting $4, 5,$ or $6$ on the first throw and $1, 2, 3,$ or $4$ on the second throw?

$A$ number $n$ is chosen at random from $\{1, 2, 3, 4, \ldots, 1000\}$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ is:

Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of $10$ will appear is

Suppose that a die (with faces marked $1$ to $6$) is loaded in such a manner that for $K = 1, 2, 3, 4, 5, 6$,the probability of the face marked $K$ turning up when the die is tossed is proportional to $K$. The probability of the event that the outcome of a toss of the die will be an even number is equal to

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the target independently,then the probability that the target would be hit is: