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Probability

This topic has 4 expert replies and 0 member replies

Probability

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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

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GMAT/MBA Expert

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Quote:
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.

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GMAT/MBA Expert

Post
The answer choices should appear as follows:

Quote:
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.

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GMAT/MBA Expert

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I thought I'd point out that Mitch's Double Matrix approach can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of 2500 people, and the two characteristics are:
- invests in municipal bonds or does not invest in invest in municipal bonds
- invests in oil stocks or does not invest in invest in oil stocks

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html

Medium Problem Solving questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/920
- http://www.beatthegmat.com/posted-speed-limit-t272374.html
- http://www.beatthegmat.com/motel-t271938.html
- http://www.beatthegmat.com/of-the-applicants-passes-a-certain-test-15-t270255.html
- http://www.beatthegmat.com/opening-night-and-late-patrons-t264869.html
- http://www.beatthegmat.com/at-least-100-students-at-a-certain-high-school-study-japanes-t274669.html
- http://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/946
- http://www.beatthegmat.com/ratio-problem-t268339.html
- http://www.beatthegmat.com/overlapping-sets-question-t265223.html
- http://www.beatthegmat.com/fractions-t264254.html
- http://www.beatthegmat.com/overlapping-sets-t264092.html
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

Easy Data Sufficiency questions
- http://www.gmatprepnow.com/module/gmat-word-problems/video/943
- http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html
- http://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- http://www.beatthegmat.com/sets-matrix-ds-t271914.html
- http://www.beatthegmat.com/each-of-people-voted-once-in-an-election-x-t271375.html
- http://www.beatthegmat.com/a-manufacturer-t270331.html
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- http://www.beatthegmat.com/double-set-matrix-question-t271423.html
- https://youtu.be/dOZ9KM1m5Hs
- http://www.beatthegmat.com/sets-t269449.html
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
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GMAT/MBA Expert

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Roland2rule wrote:
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) 9/50

B) 7/25

C) 7/20

D) 21/50

E) 27/50

The number of people who invest in ONLY municipal bonds is:

2,500 x 0.35 - 2,500 x 0.07

2,500(0.35 - 0.07) = 2,500(0.28) = 700

So, the probability that the person selected will be one who invests in municipal bonds and NOT in oils stocks is 700/2500 = 7/25

Answer: B

_________________

Jeffrey Miller
Head of GMAT Instruction
jeff@targettestprep.com



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