What is the area that is covered by putting a $8\times 6$ rectangle and a $5 \times 5$ square as shown on a table?

Arnold is studying the prevalence of three health risk factors, denoted by $A$, $B$, and $C$, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is $0.1$. For any two of the three factors, the probability that a randomly selected man has exactly these two risk factors (but not the third) is $0.14$. The probability that a randomly selected man has all three risk factors, given that he has $A$ and $B$ is $\frac{1}{3}$. Find the probability that a man has none of the three risk factors given that he does not have risk factor $A$.

Find the number of rational numbers $r$, $0 < r < 1$, such that when $r$ is written as a fraction in lowest terms, the numerator and the denominator have a sum of $1000$.