If two dice are thrown simultaneously,then the probability that the sum of the numbers which come up on the dice is more than $5$ is:

If two dice are thrown together,then the probability that the sum of the numbers appearing on them is a prime number is:

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

$A$ box contains $100$ tickets numbered $1$ to $100$. $A$ ticket is drawn at random from the box. Then the probability that the number on the ticket is a perfect square is

$A$ and $B$ toss a coin alternatively,the first to show a head being the winner. If $A$ starts the game,the chance of his winning 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 and exhaustive.