An integer $x$ is chosen at random from $1$ to $50$. The probability that $x + \frac{336}{x} \leq 50$ is

$A$ letter is chosen at random from the word $ASSASSINATION$. Find the probability that the letter is a vowel. (in $/13$)

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 and exhaustive.

Each of $a$ and $b$ can take values $1$ or $2$ with equal probability. The probability that the equation $ax^{2} + bx + 1 = 0$ has real roots is equal to

Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of $10$ will appear is

Three coins are tossed once. Let $A$ denote the event 'three heads show',$B$ denote the event 'two heads and one tail show',$C$ denote the event 'three tails show',and $D$ denote the event 'a head shows on the first coin'. Which events are simple?