$A$ die is rolled. Let $E$ be the event "die shows $4$" and $F$ be the event "die shows an even number". Are $E$ and $F$ mutually exclusive?

$A$ 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 either red or blue.

In a competition,$A, B$,and $C$ are participating. The probability that $A$ wins is twice that of $B$,and the probability that $B$ wins is twice that of $C$. Then,the probability that $A$ loses is:

Three athletes $A, B$ and $C$ participate in a race competition. The probability of winning for $A$ and $B$ is twice the probability of winning for $C$. Then the probability that the race is won by $A$ or $B$ is:

The probability that a non-leap year selected at random will have $53$ Sundays or $53$ Saturdays is

$A$ student appears for tests $I, II$ and $III$. The student is successful if he passes either in tests $I$ and $II$ or tests $I$ and $III$. The probabilities of the student passing in tests $I, II, III$ are $p, q$ and $\frac{1}{2}$ respectively. If the probability that the student is successful is $\frac{1}{2}$,then