A set $S$ contains $7$ elements. A non-empty subset $A$ of $S$ and an element $x$ of $S$ are chosen at random. Then the probability that $x \in A$ is

A coin is tossed three times, consider the following events.

$A: $ ' No head appears ',  $B:$ ' Exactly one head appears ' and  $C:$ ' Atleast two heads appear '

Do they form a set of mutually exclusive and exhaustive events?

A die has two faces each with number $^{\prime}1^{\prime}$ , three faces each with number $^{\prime}2^{\prime}$ and one face with number $^{\prime}3^{\prime}$. If die is rolled once, determine $P (2)$.

From a pack of $52$ cards two are drawn with replacement. The probability, that the first is a diamond and the second is a king, is

A bag contains $4$ white, $5$ black and $6$ red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red