Two dice are thrown simultaneously. What is the probability of obtaining a sum of the numbers less than $11$?

Two dice are thrown simultaneously. The probability of obtaining a total score of $5$ is

$A$ number $x$ is chosen at random from the set $\{1, 2, 3, 4, \dots, 100\}$. Define the event: $A =$ the chosen number $x$ satisfies $\frac{(x - 10)(x - 50)}{(x - 30)} \ge 0$. Then $P(A)$ is

$A$ 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 $3$.

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 chance of throwing a total of $7$ or $12$ with $2$ dice is: