$A$ mathematics problem is given to three students $A, B$,and $C$. The probabilities of them solving the problem are $1/2, 1/3$,and $1/4$ respectively. What is the probability that the problem is solved?

Two students,Anil and Ashima,appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10$. The probability that both will qualify the examination is $0.02$. Find the probability that only one of them will qualify the examination.

If $\frac{1+3P}{3}$ and $\frac{1-2P}{2}$ are probabilities of two mutually exclusive events,then $P$ lies in the interval.

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 the event $A$. Then the events $A$ and $B$ are

If $A$ and $B$ are events such that $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(\overline{A}) = \frac{2}{3}$,then what is the value of $P(\overline{A} \cap B)$?

$A$ card is selected from a pack of $52$ cards. How many points are there in the sample space?