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A certain club has 10 members, including Harry. One of the [#permalink]
08 Jan 2007, 23:22

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Difficulty:

55% (hard)

Question Stats:

63% (02:21) correct
37% (01:34) wrong based on 189 sessions

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

(Probability of not becoming president * prob. of becoming secretary) + (prob of not becoming president*prob. of not becoming secretary*probability of becoming treasurer)

I came to the same answer a different way and may be lucky it worked. I took prob. of sec. plus tres. 1/9+1/8 =17/72 *9/10 which is prob of not president. This equals 153/720 or .21 or 1/5.

Anyone else have a cleaner method.

hsampath- like yours better, not sure if mine is right way.

There are two scenarios:
1) Harry is NOT elected President AND is elected Secretary.
2) Harry is NOT elected President AND is not elected Secretary AND is selected Treasurer.

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

A 1/720 B 1/80 C 1/10 D 1/9 E 1/5

Not sure the OA I have is correct.

its correct.
total possibilities = 10x9x8
no of possibilities for sec. = 1x9x8
no of possibilities for tres. = 1x9x8
prob = 2(9x8)/(10x9x8) = 1/5

a certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to b the treasurer. What is the probability that Harry will be either the member chosen to be the scretary of the member chosen to be the treasurer? A. 1/720 B. 1/80 C. 1/10 D. 1/9 E. 1/5

P(secretary)=P(not Harry)*P(Harry)*P(not Harry)=(9/10)(1/9)(8/8)=1/10 P(treasurer)=P(not Harry)*P(not Harry)*P(Harry)=(9/10)(8/9)(1/8)=1/10 P(secretary OR treasurer)=P(secretary)+P(treasurer)=(1/10)+(1/10)=1/5

A certain club has 10 members, including Harry. One of the 1 [#permalink]
16 Jun 2011, 20:28

Can this be solved using symmetry rule that - each and every has equal chance of choosing specific position ... so taking Choosing Sec or Tres position would be 1/10 or 1/10 => 1/10+1/10 = 1/5

Re: A certain club has 10 members, including Harry. One of the [#permalink]
26 Nov 2011, 09:37

Can somebody explain why we use in the first part of the calculation P{that he is not secretary} =1 and in the second part P{he is not treasurer} = 1/8. Should not it be 7/8 in the first part instead of 1. because we cannot be sure that he is not chosen as secretary ????? 9/10 * 1/9 *1 + 9/10 *8/9 *1/8

Re: A certain club has 10 members, including Harry. One of the [#permalink]
19 May 2014, 09:07

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Re: A certain club has 10 members, including Harry. One of the [#permalink]
19 May 2014, 22:48

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Expert's post

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

A) 1/720 B) 1/80 C) 1/10 D) 1/9 E) 1/5

This question is much easier than it appears.

Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the treasurer is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/10+1/10=2/10.

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