Probablility

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Jinglander: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Thu Jul 22, 2010 5:40 pm; Thanked: 1 times

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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Source: Beat The GMAT — Problem Solving | Sat Jul 31, 2010 3:21 pm

KrazyKarl: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Tue Jul 27, 2010 8:37 pm; Thanked: 11 times

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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Jinglander: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Thu Jul 22, 2010 5:40 pm; Thanked: 1 times

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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KrazyKarl: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Tue Jul 27, 2010 8:37 pm; Thanked: 11 times

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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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

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)