An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

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

Two dice are thrown simultaneously. The probability of getting two numbers whose product is even is

If a die is thrown $2$ times,what is the probability of getting $4$ at least once?

Two dice are rolled. If both dice have six faces numbered $1, 2, 3, 5, 7,$ and $11,$ then the probability that the sum of the numbers on the top faces is less than or equal to $8$ is

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