Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$,then the probability of both of them occurring together is

Two dice are thrown and the sum of the numbers appeared on the dice is noted. If $A$ is the event of getting a prime number as their sum and $B$ is the event of getting a number greater than $8$ as their sum,then $P(A \cap \overline{B})=$

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

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 $/81$)