$A$ pair of dice is thrown twice in succession. The probability of getting prime numbers on both the dice in the first throw and composite numbers on both the dice in the second throw is

Three coins are tossed once. Find the probability of getting at most two tails.

The probability that a person $A$ completes a work in a given time is $\frac{2}{3}$ and the probability that another person $B$ completes the same work in the same time is $\frac{3}{4}$. If both $A$ and $B$ start doing this work at the same time,then the probability that the work is completed in the given time is

Two fair dice are thrown simultaneously. The probability of getting the same number on both dice is $......$.

If $A$ and $B$ are events of a sample space such that $P(A \cup B) = \frac{3}{4}$, $P(A \cap B) = \frac{1}{4}$, and $P(\bar{A}) = \frac{2}{3}$, then $P(\bar{A} \cap B)$ is

An integer $x$ is chosen from $1$ to $50.$ Then the probability that $x + \frac{336}{x} \le 50$ is