Let $A, B, C$ be three mutually independent events. Consider the two statements ${S_1}$ and ${S_2}$

${S_1}\,\,:\,\,A$ and $B \cup C$ are independent

${S_2}\,\,:\,\,A$ and $B \cap C$ are independent

Then

A fair coin is tossed four times, and a person win $\mathrm {Rs.}$ $1$ for each head and lose  $\mathrm {Rs.}$ $1.50$ for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.

Three coins are tossed. Describe Three events which are mutually exclusive but not exhaustive.

There are $10$ pairs of shoes in a cupboard from which $4$ shoes are picked at random. The probability that there is at least one pair, is

A pair of a dice thrown, if $5$ appears on at least one of the dice, then the probability that the sum is $10$ or greater is

The probability that a marksman will hit a target is given as $1/5$. Then his probability of at least one hit in $10$ shots, is