$A$ dice is thrown twice. The probability of getting $4, 5$ or $6$ in the first throw and $1, 2, 3$ or $4$ in the second throw 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

Two dice are thrown. The events $A$,$B$,and $C$ are as follows:
$A$: getting an even number on the first die.
$B$: getting an odd number on the first die.
$C$: getting the sum of the numbers on the dice $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A$ and $B$ are mutually exclusive.

$A$ coin is tossed three times. Consider the following events:
$A$: 'No head appears',
$B$: 'Exactly one head appears',
$C$: 'At least two heads appear'.
Do they form a set of mutually exclusive and exhaustive events?

The probability that a number selected at random from the set of numbers $(1, 2, 3, \ldots, 100)$ is a cube,is

When two dice are thrown,the probability of getting a prime number on one die and a composite number on the other is