The probability of obtaining an even prime number on each die,when a pair of dice is rolled,is . . . . . . .

Let $X$ be a set containing $n$ elements. If two subsets $A$ and $B$ of $X$ are chosen at random,what is the probability that $A$ and $B$ have the same number of elements?

Consider the experiment in which a coin is tossed repeatedly until a head comes up. Describe the sample space.

$A$ die is thrown. Find the probability of the following event: $A$ number greater than or equal to $3$ will appear.

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?

Let $A$ and $B$ be two independent events of a random experiment. If the probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occur is $\frac{1}{3}$,then the probability of occurrence of $A$ is