In a game, a man wins $Rs.\,100$  if he gets $5$ or $6$ on a throw of a fair die and loses $Rs.\,50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is

A bag contains $30$ balls numbered from $1$ to $30$, one ball is drawn randomly. The probability that number on the ball is multiple of $5$ or $7$ 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 : $A=B^{\prime}$

There are $4$ envelopes with addresses and $4$ concerning letters. The probability that letter does not go into concerning proper envelope, is

A coin is tossed twice. The probability of getting head both the times is

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

$A:$ the sum is greater than $8$,

$B : 2$ occurs on either die

$C:$ the sum is at least $ 7$ and a multiple of $3.$

Which pairs of these events are mutually exclusive ?