If $P(A^c) = 0.3$,$P(B) = 0.4$,and $P(A \cap B^c) = 0.5$,then find $P[B / (A \cup B)^c]$.

If $X$ and $Y$ are two sets such that $n(X) = 17$,$n(Y) = 23$ and $n(X \cup Y) = 38$,find $n(X \cap Y)$.

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.

Let $A$ denote the set of all $2$-digit numbers in base $10$ that are equal to four times the sum of the factorials of their digits. The sum of the numbers in $A$ is

In a committee,$50$ people speak French,$20$ speak Spanish and $10$ speak both Spanish and French. How many speak at least one of these two languages?

Let $A = \{x : |x^{2} - 10| \le 6\}$ and $B = \{x : |x - 2| > 1\}$. Then: