In a single throw of three dice,the probability of getting a sum at least $5$ is

If a year is chosen at random from the years having $53$ Sundays and $53$ Mondays,what is the probability that it is a leap year?

If the letters of the word $REGULATIONS$ are arranged in such a way that the relative positions of the letters of the word $GULATIONS$ remain the same,then the probability that there are exactly $4$ letters between $R$ and $E$ is

Let $A$ and $B$ be two independent events such that $P(B) > P(A)$. If the probability that both $A$ and $B$ happen is $\frac{1}{12}$ and the probability that neither $A$ nor $B$ happens is $\frac{1}{2}$,then:

$A$ pair of $12$-sided fair dice with faces numbered $1, 2, 3, \ldots, 12$ is rolled. The probability that the sum of the numbers appearing has a remainder of $2$ when divided by $9$ is

For the three events $A, B$ and $C$,$P$ (exactly one of the events $A$ or $B$ occurs) = $P$ (exactly one of the events $B$ or $C$ occurs) = $P$ (exactly one of the events $C$ or $A$ occurs) = $p$ and $P$ (all the three events occur simultaneously) = $p^2$,where $0 < p < 1/2$. Then the probability of at least one of the three events $A, B$ and $C$ occurring is