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Probablility

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Probablility

by Jinglander » Sat Jul 31, 2010 3:21 pm
Can someone tell me where i went wrong here

A club has 10 members. They will first pick a president then a secretary then a treasure. What is the probability that a given person is selected as secretary or treasurer.

I thought about it this way. First you much not be selected as president this is a 9/10 chance. Then you have a 1/9 and 1/8 chance to be selected as one of the other positions. so 9/10*(1/9+ 1/8)
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by KrazyKarl » Sat Jul 31, 2010 4:03 pm
I think that you're missing the fact that there's only a 8/9 chance that you're not selected as the first of the other positions (say, secretary), so the odds are really:

9/10 chance not president
1/9 chance secretary
8/9 chance not secretary * 1/8 chance that, then, you become treasurer

So a 1/9 * 9/10 chance of being secretary, or 1/10

Then a 9/10 * 8/9 * 1/8 chance that you become treasurer

That would be 1/10 + 1/10 = 2/10. Is that the right answer? It almost seems too easy when you look at it like that, but I think that was your mistake before, so this at least accounts for that.
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by Jinglander » Sat Jul 31, 2010 4:10 pm
Thats right but how do you know what order to apply the fractions any order works?
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by KrazyKarl » Sat Jul 31, 2010 4:19 pm
Well if you're multiplying the order shouldn't matter (is that the transitive property? I know there's a name for it from school), so as long as you're setting it up right you should be okay. Glad that was right! I thought I might have missed something but at least thought that I could see where the first mistake was.
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by Ian Stewart » Sat Jul 31, 2010 9:39 pm
Jinglander wrote:Can someone tell me where i went wrong here

A club has 10 members. They will first pick a president then a secretary then a treasure. What is the probability that a given person is selected as secretary or treasurer.

I thought about it this way. First you much not be selected as president this is a 9/10 chance. Then you have a 1/9 and 1/8 chance to be selected as one of the other positions. so 9/10*(1/9+ 1/8)
You can also look at this in a different way: everyone is equally likely to be chosen secretary. So the given person has a 1/10 probability of being selected as secretary. Similarly, everyone is equally likely to be chosen treasurer, so our person has a 1/10 probability of being selected treasurer. So the person has a 1/10 + 1/10 = 2/10 probability of being selected secretary or treasurer.

And KrazyKarl - I think the phrase you were looking for is 'commutative property' :) (that's not a phrase you need to know for the GMAT though)
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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