Two dice are thrown together. If the numbers appearing on the two dice are different,then what is the probability that the sum is $6$?

Each of the two boxes $P$ and $Q$ contain $100$ chits numbered from $1$ to $100$. If one chit is drawn at random from each box, then the probability that the number on the chit drawn from $P$ is the square of the number on the chit drawn from $Q$, is (in $\%$)

If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$, $P(\bar{A} \cup \bar{B}) = \frac{7}{10}$, and $P(B) = \frac{2}{5}$, then $P(A)$ equals

Out of the given $25$ consecutive positive integers, three integers are drawn. If the least integer among the given $25$ integers is an odd number, then the probability that the sum of the three integers drawn is an even number is

One die of red colour,one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled,its colour and the number on its uppermost face is noted. Describe the sample space.

In a class of $60$ students, $30$ opted for $NCC$, $32$ opted for $NSS$, and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random, find the probability that the student has opted for $NSS$ but not $NCC$.