Question

Among a group of $2,500$ people, $35$ percent invest in municipal bonds, $18$ percent invest in oil stocks, and $7$ percent invest in both municipal bonds and oil stocks. If $1$ person is to be randomly selected from the $2,500$ people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?

• A. $\frac{9}{50}$
• B. $\frac{7}{25}$
• C. $\frac{7}{20}$
• D. $\frac{21}{50}$
• E. $\frac{27}{50}$

Answer 1

The correct option is B $\frac{7}{25}$

Since there are $2,500$ people, $2,500\left(0.35\right)=875$ people invest in municipal bonds, and $2,500\left(0.07\right)=175$ of those people invest in both municipal bonds and oil stocks. Therefore, there are $875-175=700$ people who invest in municipal bonds but not in oil stocks. Probability of an event $=\frac{\text{Number of desired outcomes}}{\text{Total number of outcomes that can occur}}$

Probability of investing in municipal bonds but not in oil stocks $=\frac{700}{2,500}=\frac{7}{25}$.

The correct answer is B.