An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of the four face values obtained,the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$ is: (in $/81$)

$A$ coin is tossed. If the outcome is a head,a die is thrown. If the die shows up an even number,the die is thrown again. What is the sample space for the experiment?

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.

If $A$ and $B$ are two events,what is the probability that exactly one of them occurs?

When a pair of six-faced fair dice are thrown,the probability that the sum of the numbers on the two dice is greater than $7$ is:

The probability of a student qualifying for $IITJEE$ and $EAMCET$ are $\frac{1}{5}$ and $\frac{3}{5}$ respectively. The probability that the student qualifies for at least one of these tests is: