Let $S$ be the sample space of all five-digit numbers. If $p$ is the probability that a randomly selected number from $S$ is a multiple of $7$ but not divisible by $5$,then $9p$ is equal to.

One die and a coin (both unbiased) are tossed simultaneously. The probability of getting $5$ on the top of the die and tail on the coin is

Three coins are tossed once. Find the probability of getting at least $2$ heads.

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

If any four numbers are selected,what is the probability that the last digit of their product will be $1, 3, 5$ or $7$?

$A$ die is thrown. Describe the following events: $A$: a number less than $7$,$B$: a number greater than $7$,$C$: a multiple of $3$. Find $B \cup C$.