There are $200$ individuals with a skin disorder,$120$ had been exposed to the chemical $C_{1}$,$50$ to chemical $C_{2}$,and $30$ to both the chemicals $C_{1}$ and $C_{2}$. Find the number of individuals exposed to chemical $C_{2}$ but not chemical $C_{1}$.

In a survey of $60$ people,it was found that $25$ people read newspaper $H$,$26$ read newspaper $T$,$26$ read newspaper $I$,$9$ read both $H$ and $I$,$11$ read both $H$ and $T$,$8$ read both $T$ and $I$,and $3$ read all three newspapers. Find the number of people who read exactly one newspaper.

If the probabilities of a student succeeding in the entrance tests for institutes $A$, $B$ and $C$ are $0.6$, $0.5$ and $0.4$ respectively, while the probability of succeeding in both $A$ and $B$ is $0.3$, in both $B$ and $C$ is $0.2$, in both $A$ and $C$ is $0.2$, and in all three is $0.1$, then the probability that the student succeeds in exactly one of these tests is......

In a certain school,$74 \%$ of students like cricket,$76 \%$ of students like football,and $82 \%$ of students like tennis. Then,all three sports are liked by at least $...... \%$ of students.

Let $n(U) = 700, n(A) = 200, n(B) = 300$ and $n(A \cap B) = 100,$ then $n(A^c \cap B^c) = $

The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is