Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment

$A:$ $^{\prime}$ the sum is even $^{\prime}$.
$B:$ $^{\prime}$the sum is a multiple of $3$$^{\prime}$
$C:$ $^{\prime}$the sum is less than $4 $$^{\prime}$
$D:$ $^{\prime}$the sum is greater than $11$$^{\prime}$.

Which pairs of these events are mutually exclusive ?

On her vacations Veena visits four cities $(A,\,B ,\, C$ and $D$ ) in a random order. What is the probability that she visits $A$ either first or second?

Three coins are tossed once. Find the probability of getting atleast $2$ heads.

The probability of happening 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 happening neither $A$ nor $B$ is

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