If three students $A, B, C$ independently solve a problem with probabilitities $\frac{1}{3},\frac{1}{4}$ and $\frac{1}{5}$ respectively, then the probability that the problem will be solved is

A box contains $3$ white and $2$ red balls. A ball is drawn and another ball is drawn without replacing first ball, then the probability of second ball to be red is

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 ?

‘$A$’ draws two cards with replacement from a pack of $52$ cards and ‘$B$' throws a pair of dice what is the chance that ‘$A$’ gets both cards of same suit and ‘$B$’ gets total of $6$

The chance of getting a doublet with $2$ dice is

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 $\leq 5$

State true or false $:$ (give reason for your answer)

Statement : $A$ and $B$ are mutually exclusive