Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements :

$(S1)$ : If $P ( A )=0$, then $A =\phi$

$( S 2)$ : If $P ( A )=$, then $A =\Omega$

Then

A box contains $2$ black, $4$ white and $3$ red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence of $2$ black, $4$ white and $3$ red is

The probability of obtaining sum ‘$8$’ in a single throw of two dice

One card is drawn from a well shuffled deck of $52$ cards. If each outcome is equally likely, calculate the probability that the card will be a diamond not an ace

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.

A box contains $6$ nails and $10$ nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or is a nail