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by jamesk486 » Sun Apr 08, 2007 3:35 pm
A question from the Official Guide #7 (the diagnostic test section)

A certain club has 10 members-including Harry. One of the 10 members it be chosen at random to be president, one of the remaining 9 mimbers is to be chosen at random to be secretary, and one of the remaining 8 members is to be chosen at random to be treasurer. What is the probability that harry will be either the member chosen to be the secretary or the member chosen to be treasurer?

The explanation is pretty obscure in the book, and it said that in the case that Harry is secretary, then the probability of not being chosen for president is 9/10 (understood), for secretary 1/9, and for treasurer it would be 1-0=1==> which i DONT understand..wouldn't it be 7/8?
in the case that Harry is treasurer, then the probability of him not being secretary is 8/9, which i understand but why wouldn't it be 1-0=1 as well?
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by Cybermusings » Tue Apr 10, 2007 2:30 am
A certain club has 10 members-including Harry. One of the 10 members it be chosen at random to be president, one of the remaining 9 mimbers is to be chosen at random to be secretary, and one of the remaining 8 members is to be chosen at random to be treasurer. What is the probability that harry will be either the member chosen to be the secretary or the member chosen to be treasurer?

Chairman can be chosen from amongst 10 members in 10 ways; Secretary can be chosen from amongst 9 members in 9 ways and Treasurer can be chosen from amongst 8 members in 8 ways. Hence total number of possibilities = 10.9.8 = 720

Now Scenario I : When Harry is Secretary. It is important that he is not the Chairman. Hence possibility = 9*1*8 = 72 ways
Scenario II: When Harry is Treasurer. It is important that he is neither Chairman nor Secretary = 9*8*1 = 72 ways
Hence probability that he is either secretary or treasurer = 72 + 72 / 720 = 1/5
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by RAGS » Tue Apr 10, 2007 11:40 am
For harry to be secretary two things shouls happen
ie he should not be president which is 9/10
and now harry is secreatary probability is 1/9 ( no replacements )

So we multiply 9/10 * 1/9 =1/10


For harry to be tresureer three things should happen
ie he shouls not be president which is 9/10
he should not be secretary which is 8/9 ( no replacements)
he shouls be treasurer which is 1/8 ( no replacements )

again we multiply and get 1/10

Since what we r asked is an or condition we add the probability

ie 1/10 +1/10 =1/5
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by beeparoo » Thu May 29, 2008 11:23 am
This was an excellent question for me since I have difficulty wrapping my head around probability-type word problems.

The different answers provided by the posters above are so unique, they offer different perspectives to problem solving.

My question:
Perhaps I could pick someone's brain... In these kinds of questions, how should I remember to account for the fact that Harry is NOT chosen for president?

I ignored this point and went straight to assessing the probabilities of Harry becoming Secretary and Treasurer. Clearly the wrong approach.

Is there a general tip that I should have noticed?
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