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

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
$A:$ the sum is greater than $8$.
$B:$ $2$ occurs on either die.
$C:$ the sum is at least $7$ and a multiple of $3$.
Which pairs of these events are mutually exclusive?

$A$ bag consists of $3$ red balls,$5$ blue balls and $8$ green balls. $A$ ball is selected at random. What is the probability of not getting a blue ball?

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

An anti-aircraft gun takes four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first,second,third,and fourth shots are $0.4, 0.3, 0.2$,and $0.1$ respectively. The probability that the gun hits the plane is:

Let $A$ and $B$ be two events in a random experiment. If $P(A \cap \overline{B}) = 0.1$, $P(\overline{A} \cap B) = 0.2$ and $P(B) = 0.5$, then $P(\overline{A} \cap \overline{B}) = $