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. \(\frac{27}{50}\)

Hint:

When dealing with overlapping sets or Venn diagram problems, the key is to use the formula: Total = Group1 + Group2 - Both + Neither. To find the "Only Group1" portion, calculate Group1 - Both.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a probability problem involving overlapping sets (people investing in bonds, stocks, or both). We need to find the probability of selecting a person who belongs to one set (municipal bonds) but not the other (oil stocks).
Step 2: Key Formula or Approach:
Let M be the set of people who invest in municipal bonds, and O be the set of people who invest in oil stocks. We are looking for the percentage of people who invest only in municipal bonds. This can be found by taking the total percentage of people who invest in municipal bonds and subtracting the percentage of people who invest in both.
\[ P(\text{Only M}) = P(\text{M}) - P(\text{M and O}) \] The probability of an event is equal to the proportion (or percentage) of the group that satisfies the condition.
Step 3: Detailed Explanation:
We are given the following percentages:
Percentage investing in municipal bonds, \(P(\text{M}) = 35%\).
Percentage investing in oil stocks, \(P(\text{O}) = 18%\).
Percentage investing in both, \(P(\text{M and O}) = 7%\).
We want to find the percentage of people who invest in municipal bonds but not in oil stocks. This corresponds to the \(P(\text{Only M})\).
\[ P(\text{Only M}) = 35% - 7% = 28% \] The probability of selecting a person from this group is simply this percentage expressed as a fraction.
\[ \text{Probability} = 28% = \frac{28}{100} \] Now, we simplify the fraction: \[ \frac{28}{100} = \frac{14}{50} = \frac{7}{25} \] Step 4: Final Answer:
The probability that the selected person invests in municipal bonds but NOT in oil stocks is \(\frac{7}{25}\). Note that the total number of people (2,500) is extra information and not needed to solve the problem since the data is given in percentages.