If $A$ and $B$ are events such that $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(\overline{A}) = \frac{2}{3}$,then what is the value of $P(\overline{A} \cap B)$?

$A$ bag contains $3$ white,$2$ blue,and $5$ red balls. One ball is drawn at random from this bag. The probability that the ball drawn is not red is

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements:
$(S1) : \text{If } P(A) = 0, \text{ then } A = \phi$
$(S2) : \text{If } P(A) = 1, \text{ then } A = \Omega$
Then:

$A$ man alternately tosses a coin and throws a dice,beginning with the coin. The probability that he gets a head in the coin before he gets a $5$ or $6$ in the dice is

The probability that a randomly selected $2$-digit number belongs to the set $\{n \in N : (2^{n}-2) \text{ is a multiple of } 3\}$ is equal to:

In a certain lottery $10,000$ tickets are sold and $10$ equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket?