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# Among a group of 2,500 people, 35 percent invest in

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

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14 Jun 2012, 01:49
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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 but NOT in oil stocks?

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

Diagnostic Test
Question: 4
Page: 20
Difficulty: 650
[Reveal] Spoiler: OA

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

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14 Jun 2012, 01:49
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SOLUTION

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

Given:
$$0.35*2,500=875$$ invest in municipal bonds;
$$0.07*2,500=175$$ invest in in both municipal bonds and oil stocks;

Therefore $$875-175=700$$ invest in municipal bonds but NOT in in oil stocks. (Or directly: 35%-7%=28% of 2,500, which is 700, invest in municipal bonds but NOT in in oil stocks).

$$P=\frac{Favorable}{Total}=\frac{700}{2,500}=\frac{7}{25}$$.

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

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14 Jun 2012, 05:09
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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 but NOT in oil stocks?

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

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.

As per the attached venn diagram, we have to find the number of people in shaded portion.
=35%-7%=28%

Thus, probability = 0.28 = 7/25

(2,500 people, 18 percent invest in oil stocks is not required.)

Attachments

m.jpg [ 9.55 KiB | Viewed 34568 times ]

Last edited by cyberjadugar on 09 Jul 2012, 00:04, edited 1 time in total.

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

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14 Jun 2012, 05:50
People with Municipal Bond but not with Oil Stock
= People with Municipal Bond and Oil stock – People with Municipal Bond but not Oil S
= 35%of 2500 – 7% of 2500
= 700
Now,
P ( one person investing in Municipal Bond but not in Oil Stock ) = 700 /2500 = 7/25

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

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14 Jun 2012, 19:19
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Percentage investing in Municipal bonds = 35%
Percentage investing in both = 7%
Percentage investing in ONLY Municipal bonds = (35-7)% = 28%

Therefore, Probability of selecting one who invests Only in Municipal bonds = 28% = 28/100 = 7/25.

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

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16 Jun 2012, 02:52
Difficulty level 600+.

Probability of percentage invested in MB/ Total

35%-7%=28% of 2500= 700

P= 700/2500= 7/25

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

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18 Jun 2012, 06:07
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For this type of question, I sometimes use a 2X2 table approach. The table is just an organized summary of the Venn diagram.
Since in this case a probability is required, there is no need to calculate actual numbers. So, using percentages, we can fill out the table (see attached image). I started with 35, 18 and 7, then for example 11=18-7, 28=35-7, 82=100-18, 54=82-28, 65=100-35. There is more than one possible sequence. Necessarily, one must get the sum in the bottom row and that in the rightmost column exactly 100.
In fact, you don't need to fill out the whole table, once you have that Municipal and noOil represents 28%, you are done. I present the whole table just to illustrate the use of it.

So, those who invest in Municipal and noOil stocks represent 28%=28/100=7/25.

Correct asnwer is B.
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Last edited by EvaJager on 18 Jun 2012, 07:14, edited 1 time in total.

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11 Jun 2015, 19:43
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LouieV wrote:
Hello everyone and thank you for this forum!!!

I admit it has been a few years since I've sat down to attack standardized test, but my GOODNESS ! Can someone please lend some wisdom on this problem from TOG 2016 pg 20 #4.

Among a group of 2500 people, 35% invest in municipal bonds, 18% invest in oil stocks, and 7% invest in both municipal bonds and oil stocks. If 1 person is randomly selected from the 2500 people, what is the probability that the person 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

So this question actually pertains to overlapping sets.

Say, there are 100 people instead (since we have percentages)
Number of people investing in MB = 35
Number of people investing in OS = 18
Number of people investing in both = 7

So how many people invest in MB but not OS? 35 invest in MB but 7 invest in both (so out of 35, 7 invest in OC too). We need to remove these 7 since we need the number of people who invest in MB only. We get 28.
So 28 out of 100 people invest in only MB. So out of 100, if we pick one person, the probability that he invests in MB only is 28/100 = 7/25

The probability remains same no matter how many people there are - 100 or 2500 or 500000 etc.

Check out overlapping sets: http://www.veritasprep.com/blog/2012/09 ... ping-sets/
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11 Jun 2015, 19:49
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LouieV wrote:
Hello everyone and thank you for this forum!!!

I admit it has been a few years since I've sat down to attack standardized test, but my GOODNESS ! Can someone please lend some wisdom on this problem from TOG 2016 pg 20 #4.

Among a group of 2500 people, 35% invest in municipal bonds, 18% invest in oil stocks, and 7% invest in both municipal bonds and oil stocks. If 1 person is randomly selected from the 2500 people, what is the probability that the person 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

Total People = 2500 people

35% invest in municipal bonds, i.e Probability of Investing in Mutual Bonds = 0.35
i.e. i.e Probability of NOT Investing in Mutual Bonds = 0.65

18% invest in oil stocks i.e Probability of Investing in Oil stock = 0.18
i.e Probability of NOT Investing in Oil stock = 0.82

7% invest in both municipal bonds and oil stocks = 0.07

i.e. we can conclude that Probability of NOT investing in any one of them = 1-(0.35+0.18+0.07) = 0.54

Probability of Investing in Mulual Bond but NOT in Oil Stock = 0.82-0.54 = 0.28 = 28/100 = 7/25

[Reveal] Spoiler:
B

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11 Jun 2015, 20:46
Thank you for explaining this in such simple terms Karishma. GMATinsight, the visual was definitely a big help in allowing me to see the arithmetic behind the words. I was stomped, but I'm sure my gears will get back to speed as I progress in my preparation. THANKS EVERYONE!

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

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04 Sep 2015, 00:59
The fastest way is from Bunuel, but in this case I would stay with percents, as it is easier to calculate: 35%-7%(overlap)=28% --> 28%/100%=7/25
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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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04 Sep 2015, 07:16
The piece of information that states that "there are 2,500 people" is completely irrelevant, right?
In other words you can yield the correct answer without that piece of data.
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Among a group of 2,500 people, 35 percent invest in [#permalink]

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07 Sep 2015, 10:53
No need to calculate number of people

Both OS and Muni: 7%, therefore, Muni only: 28% and OS only:11%

Muni Only / All = 28%/1 >> 7/25
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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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08 Dec 2015, 08:29
Bunuel 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 but NOT in oil stocks?

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

Diagnostic Test
Question: 4
Page: 20
Difficulty: 650

For this Q - I was thinking why cant we assume that "35%" mentioned only include people that invest in municipal bonds. But Karishma from Veriats cleared the doubt. ONLY should have been mentioned - if that was the case. Below excerpts of her reply -
"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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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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17 Jan 2016, 06:44
Question - why isn't it 0.35 * 0.82 (the number of people who don't invest in oil) ?

Thanks much.

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

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17 Jan 2016, 07:08
nellietyf wrote:
Question - why isn't it 0.35 * 0.82 (the number of people who don't invest in oil) ?

Thanks much.

Because those 82% people also include people who do not go for either the municipal bonds or the stocks. Refer to the attached figure.

Text in red : calculated, text in black: calculated.

Attachment:

2016-01-17_10-07-18.jpg [ 22.63 KiB | Viewed 1866 times ]

Thus the required probability =700/2500 = 7/25.

B is thus the correct answer.

Hope this helps.

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

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20 Sep 2016, 12:48
Why didn't we say: P( bonds only) & P(not oil), which is P(bonds only) & P(1- p(oil))??
Isn't it the translation of NOT oil?

This is contradicting with solution of this OG PS question:

215- Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

The solution considered the p(not zelda)!
I am confused.

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

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11 Dec 2017, 22:23
People with Municipal Bond and Oil stock – People with Municipal Bond but not Oil S
= 35%of 2500 – 7% of 2500
= 700
700 /2500 = 7/25 Answer B
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Re: Among a group of 2,500 people, 35 percent invest in   [#permalink] 11 Dec 2017, 22:23
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