Problem Solving

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 and NOT in oils stocks?

A) 950950

B) 725725

C) 720720

D) 21502150

E) 2750

OA is B
What is the best method to solve this? An Expert contribution will be appreciated. Thanks

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 and NOT in oils stocks?

A) 950950

B) 725725

C) 720720

D) 21502150

E) 2750

OA is B
What is the best method to solve this? An Expert contribution will be appreciated. Thanks

Hi Roland2rule,
Let's take a look at your question.

Total people = 2500
35% people invest in municipal bonds, therefore,
Number of people who invest in municipal bonds = 2500 * 35/100 = 875

Number of people who invest in oil stocks = 2500*18/100 = 450
Number of people who do not invest in oil stocks = 2500 - 450 = 2050

The number of people who invest in both municipal bonds and oil stocks = 2500 * 7/100 = 175

Let's write all this information in a two way table.
$$ \text{ Oil Not Oil Total}$$
$$ \text{Municipal 175 700 875}$$
$$ \text{Not Municipal 275 1350 1625}$$
$$ \text{Total 450 2050 2500}$$
We need to find the probability that the person selected will be one who invests in municipal bonds and NOT in oils stocks.
We can see in the table that there are 700 people who invest in municipal bonds and NOT in oils stocks.

Therefore,
P(selecting a person who invest in municipal bonds and NOT in oils stocks) = 700/2500 = 7/25

Therefore, Option B is correct.

Hope this helps.
I am available if you'd like any follow up.

The answer choices should appear as follows:

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) 9/50
(B) 7/25
(C) 7/20
(D) 21/50
(E) 27/50

This is an EITHER/OR problem.
Everyone invests EITHER in stocks OR not in stocks.
Everyone invests EITHER in bonds OR not in bonds.
To organize the data in an either/or problem, use a DOUBLE-MATRIX.
Let S = stocks, NS = not stocks, B = bonds, NB = not bonds.
The following matrix is yielded:


Since the answer choices are FRACTIONS, the total number of people can be ANY VALUE.
Let the total number of people = 100:


35 percent invest in municipal bonds.
18 percent invest in oil stocks.
The following matrix is yielded:


7 percent invest in both municipal bonds and oil stocks.
The following matrix is yielded:


What is the probability that the person selected will be one who invests in municipal bonds and NOT in oils stocks?
(bonds but not stocks)/(total) = 28/100 = 7/25.

The correct answer is B.