$A$ fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is $3$.

In a random experiment of selecting a ticket from $50$ tickets numbered $00, 01, 02, 03, ..., 47, 49$,if a ticket is selected such that the product of its digits is $0$,what is the probability that the sum of its digits is $8$?

Three coins are tossed once. Find the probability of getting $3$ heads.

What is the probability that a randomly selected leap year has $53$ Sundays or $53$ Mondays? Express your answer as the numerator of the fraction (in $/7$).

If $X_1, X_2, \ldots, X_n$ are $n$ independent events such that $P(X_r) = \frac{1}{r+1}$ for $r = 1, 2, \ldots, n$,then the probability that none of the $n$ events occur is

The probability that a person $A$ completes a work in a given time is $\frac{2}{3}$ and the probability that another person $B$ completes the same work in the same time is $\frac{3}{4}$. If both $A$ and $B$ start doing this work at the same time,then the probability that the work is completed in the given time is