The probability of a sure event is

If a number $x$ is drawn randomly from the set of numbers $\{1, 2, 3, \ldots, 50\}$, then the probability that the number $x$ satisfies the inequation $x + \frac{10}{x} \leq 11$ is

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice and $E_k = \{(a, b) \in S : ab = k\}$. If $p_k = P(E_k)$, then which of the following is correct?

$A$ die is rolled. Let $E$ be the event "die shows $4$" and $F$ be the event "die shows an even number". Are $E$ and $F$ mutually exclusive?

What is the probability that when one die is thrown,the number appearing on top is even?

The probability that Ajay will not appear in the $JEE$ exam is $p = \frac{2}{7}$,while the probability that both Ajay and Vijay will appear in the exam is $q = \frac{1}{5}$. Then the probability that Ajay will appear in the exam and Vijay will not appear is: