The probabilities of three students solving a question are $\frac{1}{2}, \frac{1}{4},$ and $\frac{1}{6}$ respectively. What is the probability that the question is solved?

$A$ set $S$ contains $7$ elements. $A$ non-empty subset $A$ of $S$ and an element $x$ of $S$ are chosen at random. Then the probability that $x \in A$ is

Two dice are thrown and the sum of the numbers appeared on the dice is noted. If $A$ is the event of getting a prime number as their sum and $B$ is the event of getting a number greater than $8$ as their sum,then $P(A \cap \overline{B})=$

If two dice are thrown simultaneously,then the probability that $1$ comes on the first die is

The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively. Then,the probability that only one of them will be alive at the end of the year is

Each of the two boxes $A$ and $B$ contain $10$ chits numbered $1$ to $10$. If one chit is drawn at random from each of $A$ and $B$,then the probability that the number on the chit drawn from $A$ is smaller than the number on the chit drawn from $B$,is