Three persons work independently on a problem. If the respective probabilities that they will solve it are $\frac{{1}}{{3}} , \frac{{1}}{{4}}$ and $\frac{{1}}{{5}}$, then the probability that none can solve it

Three coins are tossed once. Let $A$ denote the event ' three heads show ', $B$ denote the event ' two heads and one tail show ' , $C$ denote the event ' three tails show and $D$ denote the event 'a head shows on the first coin '. Which events are mutually exclusive ?

From a pack of $52$ cards one card is drawn at random, the probability that it is either a king or a queen is

Three coins are tossed once. Find the probability of getting atmost two tails.

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 $\leq 5$

Describe the events $A^{\prime }.$