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

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

A bag contains $5$ white, $7$ red and $8$ black balls. If four balls are drawn one by one without replacement, what is the probability that all are white

The probabilities of winning the race by two athletes $A$ and $B$ are $\frac{1}{5}$ and $\frac{1}{4}.$ The probability of winning by neither of them, is

The probability of getting a number greater than $2$ in throwing a die is

Find the probability that the two digit number formed by digits $1, 2, 3, 4, 5$ is divisible by $4$ (while repetition of digit is allowed)