The probability of happening an event $A$ in one trial is $0.4$. The probability that the event $A$ happens at least once in three independent trials 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 : $A=B^{\prime}$

Three coins are tossed. Describe Two events which are mutually exclusive but not exhaustive.

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

If in a lottary there are $5$ prizes and $20$ blanks, then the probability of getting a prize is

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