An integer is chosen at random and squared. The probability that the last digit of the square is $1$ or $5$ is

$A$ number $n$ is chosen at random from the natural numbers $2$ to $1001$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ 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?

Let $A$ and $B$ be two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$,and $P(\bar{A}) = \frac{1}{4}$,where $\bar{A}$ stands for the complement of event $A$. Then events $A$ and $B$ are

Two dice are rolled. If both dice have six faces numbered $1, 2, 3, 5, 7, 11$,then the probability that the sum of the numbers on the uppermost faces is a prime number is:

$A$ problem of mathematics is given to three students whose chances of solving the problem are $\frac{1}{3}$,$\frac{1}{4}$,and $\frac{1}{5}$ respectively. The probability that the question will be solved is