In a single throw of a fair die,what is the probability of getting a number less than $7$?

Two dice are thrown. If the first die shows $5$,what is the probability that the sum of the numbers on both dice is $8$ or more than $8$?

If $A$ and $B$ are two events such that $P(A) = \frac{1}{4}$,$P(B) = \frac{1}{2}$,and $P(A \cap B) = \frac{1}{8}$,find $P(\text{not } A \text{ and not } B)$.

If $\frac{1 + 3p}{3}, \frac{1 - p}{4}$ and $\frac{1 - 2p}{2}$ are the probabilities of three mutually exclusive events,then the set of all values of $p$ is

In a simultaneous throw of a pair of dice,the probability of getting a total more than $7$ is

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