The probability that two randomly selected subsets of the set $\{1, 2, 3, 4, 5\}$ have exactly two elements in their intersection is:

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up $4$,$E_2$ is the event that die $B$ shows up $2$,and $E_3$ is the event that the sum of numbers on both dice is odd,then which of the following statements is $NOT$ true?

From $10,000$ lottery tickets numbered from $1$ to $10,000$,one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by $20$?

Three identical dice are rolled. The probability that the same number will appear on each of them is:

Two integers $x$ and $y$ are chosen with replacement from the set $\{0, 1, 2, 3, \ldots, 10\}$. Then the probability that $|x-y| > 5$ is:

$A$ number $x$ is chosen at random from the set $\{1, 2, 3, 4, ......, 100\}$. Then the probability of the event that the chosen number $x$ satisfies the inequality $\frac{(x - 10)(x - 50)}{(x - 30)} \geqslant 0$ is: