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 bag contains $9$ discs of which $4$ are red, $3$ are blue and $2$ are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be not blue,

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?

Two cards are drawn from a pack of $52$ cards. What is the probability that one of them is a queen and the other is an ace

A number is chosen at random from the set $\{1,2,3, \ldots, 2000\}$. Let $p$ be the probability that the chosen number is a multiple of $3$ or a multiple of $7$ . Then the value of $500\ p$  is. . . . . . 

Three fair coins are tossed. If both heads and tails appears, then the probability that exactly one head appears, is