$A$ die has two faces each with number $1$,three faces each with number $2$,and one face with number $3$. If the die is rolled once,determine $P(2)$.

Let $A$ be the event that the absolute difference between two randomly chosen real numbers in the sample space $[0, 60]$ is less than or equal to $a$. If $P(A) = \frac{11}{36}$,then $a$ is equal to $...............$.

One card is drawn from each of two ordinary packs of $52$ cards. The probability that at least one of them is an ace of hearts is:

The event $A$ is independent of itself if and only if $P(A) = $

If two integers are chosen at random,what is the probability that their product is an even integer?

$A$ problem in mathematics is given to $4$ students whose chances of solving it individually are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4},$ and $\frac{1}{5}.$ The probability that the problem will be solved by at least one student is