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Among a group of 2,500 people, 35 percent invest in muni.... [#permalink]

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09 Jun 2011, 19:17

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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?

Hi, I had a doubt in the answer given by OG 12 for a probability related PS question. " The question is, 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?

The answer is 7/25.

The explanation given is Since there are 2500 people, 2500(.35) = 875 people invest in municipal bonds, and 2,500(.07) = 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 investing in municipal bonds but not in oil stocks = 700/2500 = 7/25 "

My doubt is, Cant we consider the 35 percent who have invested in municipal bonds and the 7 percent who have invested in both bonds and oil, as to separate groups rather than considering the people in the 7 percent to be a part of the 35 percent group?

Cant we just take 875/2500 = 7/20, as the answer?

Why should we do the 875-175 operation, when it 35 percent of people are only invested in municipal bonds?

Sorry for the long post.

When they say '35% invest in municipal bonds', this number includes the 7% people who invest in both (since they obviously invest in municipal bonds too). Since you want to ignore the people who invest in stocks, from 35%, you subtract 7% to get 28%. Hence, 28/100 = 7/25 of the total people invest in ONLY municipal bonds.
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35% includes both municipal bond investors + oil investors. So you need to take out 7% which overlaps with 35% as you want to be sure that your 35% doesnt include any oil investor. With 28% you are 100% sure that these are all municipal bond investors
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Thanks a lot for your answers. It looks like it is a standard question.

"35% includes both municipal bond investors + oil investors. " Could there be questions where the the 35% and the 7% should be considered as mutually exclusive when finding the answers?

Thanks a lot for your answers. It looks like it is a standard question.

"35% includes both municipal bond investors + oil investors. " Could there be questions where the the 35% and the 7% should be considered as mutually exclusive when finding the answers?

Yes, if they say, "35% invest in municipal bonds only and 7% invest in both," then the two are mutually exclusive.
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This question will be better understood if you try the Venn Diagram approach.

I used a matrix. Maybe it was the wrong approach but I got it right. Then I got 28% for Muncipal Bonds but not Oil. Lets say there are 100 people (easier to calculate, even if you don't need it) 28% out of 100 is 7/25.

Re: Among a group of 2,500 people, 35 percent invest in muni.... [#permalink]

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28 May 2012, 10:31

I understand the math behind this...easy problem...but I think this is poorly worded. How can you come to the absolute conclusion that the 7% in both is included in the 35% and 18%? When reading it, I see them listing it out as if it was a 3rd group instead of a shared group.

Re: Among a group of 2,500 people, 35 percent invest in muni.... [#permalink]

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10 Dec 2012, 18:43

This problem can be handled by a straightforward matrix, the only thing that is semi-difficult is the calculations, but some handy multiplication tricks borrowed from some case interviewing skills help.

35% of 2500 is: 10% of 2500 = 250 * 3 = 750 + 1/2 of 250 = 875. 35% MB

18% of 2500 is 10% of 2500 = 250 * 2 - 1% of 2500 * 2 = 450 = 18% oil

7% of 2500 is 1% of 2500 = 25 * 7 = 175 = 7% oil.

875-175 = 700

700 divided by total investment possibilities (2500) = 7 / 25

This problem can be handled by a straightforward matrix, the only thing that is semi-difficult is the calculations, but some handy multiplication tricks borrowed from some case interviewing skills help.

35% of 2500 is: 10% of 2500 = 250 * 3 = 750 + 1/2 of 250 = 875. 35% MB

18% of 2500 is 10% of 2500 = 250 * 2 - 1% of 2500 * 2 = 450 = 18% oil

7% of 2500 is 1% of 2500 = 25 * 7 = 175 = 7% oil.

875-175 = 700

700 divided by total investment possibilities (2500) = 7 / 25

You don't have to do any calculations. The data is given in percentages and you are asked the probability. You don't need any concrete numbers i.e. you don't need to use 2500. Check the solutions given above.
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Re: Among a group of 2,500 people, 35 percent invest in muni.... [#permalink]

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10 Dec 2012, 20:02

VeritasPrepKarishma wrote:

AlyoshaKaramazov wrote:

This problem can be handled by a straightforward matrix, the only thing that is semi-difficult is the calculations, but some handy multiplication tricks borrowed from some case interviewing skills help.

35% of 2500 is: 10% of 2500 = 250 * 3 = 750 + 1/2 of 250 = 875. 35% MB

18% of 2500 is 10% of 2500 = 250 * 2 - 1% of 2500 * 2 = 450 = 18% oil

7% of 2500 is 1% of 2500 = 25 * 7 = 175 = 7% oil.

875-175 = 700

700 divided by total investment possibilities (2500) = 7 / 25

You don't have to do any calculations. The data is given in percentages and you are asked the probability. You don't need any concrete numbers i.e. you don't need to use 2500. Check the solutions given above.

yours is definitely more elegant, no question. just another way to skin the cat, I suppose.

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