A pair of a dice thrown, if $5$ appears on at least one of the dice, then the probability that the sum is $10$ or greater is

The probabilities of winning the race by two athletes $A$ and $B$ are $\frac{1}{5}$ and $\frac{1}{4}.$ The probability of winning by neither of them, is

A coin is tossed $4$ times. The probability that at least one head turns up 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 and exhaustive

Let $A$ be a set of all $4 -$digit natural numbers whose exactly one digit is $7 .$ Then the probability that a randomly chosen element of  $A$ leaves remainder $2$ when divided by $5$ is ..... .

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