Two dice are thrown. The probability that the sum of the points on two dice will be $7$, is

A coin is tossed. If it shows a tail, we draw a ball from a box which contains $2$ red and $3$  black balls. If it shows head, we throw a die. Find the sample space for this experiment.

An experiment consists of rolling a die and then tossing a coin if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

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

The number $1,\,2,\,3$ and $4$ are written separately on four slips of paper. The slips are put in a box and mixed thoroughly, A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.

$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P ( A \cup B )$.