The probability that a randomly selected $2$-digit number belongs to the set $\{n \in N : (2^{n}-2) \text{ is a multiple of } 3\}$ is equal to:

$A$ card is drawn at random from a pack of $100$ cards numbered $1$ to $100$. The probability of drawing a number which is a perfect square is

$A$ 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?

For two events $A$ and $B$,if $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(A') = \frac{2}{3}$,then find $P(A' \cap B)$.

In a class of $60$ students, $30$ opted for $NCC$, $32$ opted for $NSS$, and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random, find the probability that the student has opted for $NSS$ but not $NCC$.

$A$ fair die is rolled once. Let $A$ be the event of getting an integer greater than $3$ and $B$ be the event of getting an integer less than $5$. Find $P(A \cup B)$.