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 simple ?

For independent events ${A_1},\,{A_2},\,……….,{A_n},$ $P({A_i}) = \frac{1}{{i + 1}},$ $i = 1,\,\,2,\,……,\,\,n.$ Then the probability that none of the event will occur, is

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

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 : $A=B^{\prime}$

A fair coin is tossed repeatedly. If tail appears on first four tosses then the probability of head appearing on fifth toss equals