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Probability

by cypherskull » Mon May 07, 2012 11:05 am
among a group of 2500 people, 35% invest in municipal bonds, 18% in oil stocks and 7% in both. If 1 person is to be selected at random from 2500 people, what is the probability that the person selected will be one who invests in municipal bonds and not in oil stocks?

a) 9/50
b) 7/25
c) 7/20
d) 21/50
e) 27/50

I got the answer correct. That is B. However, I tried doing it another way first - that is by calculating the probability of selecting a person investing in oil stocks and subtracting it from 1. I got the answer as 41/50 (9/50 being the calculated probability of selecting an individual investing in oil stocks). Not sure where did I go wrong here.
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by aneesh.kg » Mon May 07, 2012 11:30 am
You also have to subtract those people who invest in neither Municipal bonds nor Oil Stocks.
The unfavourable probability includes the probability of selecting an Oil stocks person as well as the probability of selecting a person who has invested in neither of the two.

Solution:

Required Probability =
1 - (Probability that the person who invests in Municipal Bonds is not selected)
1 - [P(Oil stocks) + P(neither Municipal bonds nor Oil stocks)]
1 - [18/100 + (100 - 46)/100]
1 - 72/100
7/25
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by cypherskull » Mon May 07, 2012 11:40 am
That helped...Thanks a lot..! :)
Regards,
Sunit

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by redng » Tue May 08, 2012 8:09 pm
On the GMAT, how can you tell if the 7% is or isn't part of the 35% and 18%? Is there 175 who invest in both, 875 only in muni, and 450 only in oil, or 175 both 700 muni only and 275 oil only?

And if it's the latter, can you just divide 2500 by 700?
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by mdavidm_531 » Tue May 08, 2012 8:28 pm
redng wrote:On the GMAT, how can you tell if the 7% is or isn't part of the 35% and 18%? Is there 175 who invest in both, 875 only in muni, and 450 only in oil, or 175 both 700 muni only and 275 oil only?

And if it's the latter, can you just divide 2500 by 700?
In cases such as this, I prefer using a double-matrix.

Check this out:

Image

I prefer this method, although took me more than 2 minutes (because of computation of percentages)
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by aneesh.kg » Tue May 08, 2012 8:34 pm
Hi,

This problem, just like a GMAT problem, gives a clear indication that 7% is a part of 35% as well as 28% when it says:
"..and 7% in both. If.."

Yes, it is the latter of the two cases mentioned by you. And the easiest way is to just divide 7% by 25%, without even converting the percentages into number.

The method shown in my post above was an Alternate and longer method, because Sunit wanted to do it that way.
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by redng » Tue May 08, 2012 8:42 pm
Image

so you would never interpret it as this? thanks!
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by mdavidm_531 » Tue May 08, 2012 8:45 pm
redng wrote:Image

so you would never interpret it as this? thanks!
Check out the image I posted above. I think it's all about reading the problem critically (will help you with critical reasoning lol)
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by GMATGuruNY » Wed May 09, 2012 2:26 am
cypherskull wrote:among a group of 2500 people, 35% invest in municipal bonds, 18% in oil stocks and 7% in both. If 1 person is to be selected at random from 2500 people, what is the probability that the person selected will be one who invests in municipal bonds and not in oil stocks?

a) 9/50
b) 7/25
c) 7/20
d) 21/50
e) 27/50
Ignore the total number of people given (2500).
The fraction who invest in bonds but not stocks will be the same, regardless of the total number of people.

Let the total number of people = 100.
Then the total number who invest in bonds = 35.
Of these 35, 7 invest in BOTH bonds and stocks, implying that the number who invest in bonds but NOT stocks = 35-7 = 28.
Thus:
P(someone invests in bonds but not stocks) = 28/100 = 14/50 = 7/25.

The correct answer is B.
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by bryan88 » Wed May 09, 2012 9:22 am
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