$A$ coin is tossed $m + n$ times,where $m \ge n.$ The probability of getting at least $m$ consecutive heads is

In a throw of three dice,the probability that at least one die shows up $1$,is

$A$ and $B$ each select one number at random from the distinct numbers $1, 2, 3, \ldots, n$. The probability that the number selected by $A$ is less than the number selected by $B$ is $\frac{1009}{2019}$. The probability that the number selected by $B$ is the number immediately next to the number selected by $A$ is:

The probability that a year selected at random will have $53$ Mondays is

$A, B, C$ try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are $\frac{3}{4}, \frac{1}{2}, \frac{5}{8}$. The probability that the target is hit by $A$ or $B$ but not by $C$ is

Let the mean and variance of $7$ observations $2, 4, 10, x, 12, 14, y$ (where $x > y$) be $8$ and $16$ respectively. Two numbers are chosen from the set $\{1, 2, 3, x-4, y, 5\}$ one after another without replacement. Then the probability that the smaller number among the two chosen numbers is less than $4$ is: