The probabilities of two events $A$ and $B$ are $0.25$ and $0.50$ respectively. The probability of both $A$ and $B$ occurring simultaneously is $0.14$. What is the probability that neither $A$ nor $B$ occurs?

If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$, $P(\bar{A} \cup \bar{B}) = \frac{7}{10}$, and $P(B) = \frac{2}{5}$, then $P(A)$ equals

Suppose $3$ bulbs are selected at random from a lot. Each bulb is tested and classified as defective $(D)$ or non-defective $(N)$. Write the sample space of this experiment.

Let $E_{1}, E_{2}, E_{3}$ be three mutually exclusive events such that $P(E_{1}) = \frac{2+3p}{6}$,$P(E_{2}) = \frac{2-p}{8}$,and $P(E_{3}) = \frac{1-p}{2}$. If the maximum and minimum values of $p$ are $p_{1}$ and $p_{2}$,then $(p_{1} + p_{2})$ is equal to.

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A$ and $B$ are mutually exclusive and exhaustive.

$A$ card is drawn at random from a pack of $52$ cards. The probability that the drawn card is a court card,i.e.,a jack,a queen,or a king,is: