The probability of happening of an event $A$ is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events,then the probability of neither $A$ nor $B$ 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

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

Let $A = \{1, 3, 5, 7, 9\}$ and $B = \{2, 4, 6, 8\}$. If an ordered pair $(a, b)$ is chosen at random from the Cartesian product $A \times B$,what is the probability that $a + b = 9$?

Three coins are tossed once. Let $A$ denote the event 'three heads show',$B$ denote the event 'two heads and one tail show',$C$ denote the event 'three tails show',and $D$ denote the event 'a head shows on the first coin'. Which events are simple?

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