Consider the experiment of rolling a die. Let $A$ be the event 'getting a prime number ', $B$ be the event 'getting an odd number '. Write the sets representing the events $A$ or $B$.

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

A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is $1/4$ and that of the woman's selection is $1/3$. What is the probability that none of them will be selected

A single letter is selected at random from the word “$PROBABILITY$”. The probability that the selected letter is a vowel is

Three coins are tossed. Describe Three events which are mutually exclusive and exhaustive.

A coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed $5$ times is