In an experiment of tossing a coin and a fair die,the probability of getting a head on the coin and $6$ on the die is ..........

If $A, B$ and $C$ are mutually exclusive and exhaustive events of a random experiment such that $P(A) = \frac{2}{3} P(B)$ and $P(B) = 2 P(C)$,then $P(A \cup C) =$

If two dice are thrown together,then the probability that the sum of the numbers appearing on them is a prime number is:

Let $S$ be a set of $5$ elements and $P(S)$ denote the power set of $S$. Let $E$ be an event of choosing an ordered pair $(A, B)$ from the set $P(S) \times P(S)$ such that $A \cap B = \varnothing$. If the probability of the event $E$ is $\frac{3^p}{2^q}$, where $p, q \in N$, then $p+q$ is equal to

$A$ 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.

Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in the exam is $\frac{1}{4}$ and the probability that the second student gets qualified in the same exam is $\frac{2}{5}$,then the probability that at least one of them gets qualified in that exam is