Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

61% (02:49) correct
39% (01:59) wrong based on 1391 sessions

HideShow timer Statistics

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 be either the member chosen to 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

Diagnostic Test Question: 7 Page: 21 Difficulty: 650

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 be either the member chosen to 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.

Re: A certain club has 10 members, including Harry. One of the [#permalink]

Show Tags

25 Jun 2012, 04:35

15

This post received KUDOS

6

This post was BOOKMARKED

Hi,

Difficulty level = 650

Probability = (Favorable cases)/(total cases)

Case 1: When Harry is chosen as secretary probability = 9/10 * 1/9 * 8/8 = 1/10 (9 available for post of president out of 10, then Harry has to be chosen out of 9, and finally out of 8 anyone can be treasurer)

Case 2: When Harry is chosen as treasurer probability = 9/10 * 8/9 * 1/8 = 1/10 (9 available for post of president out of 10, then out of 8 anyone can be secretary, and finally Harry has to be treasurer)

probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer = 1/10 + 1/10 =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 be the treasurer. What is the probability that Harry will be either the member chosen to 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.

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

But I am confused since:

P(secretary OR treasurer)=P(secretary)+P(treasurer)-P(secretary and treasurer)+ P(Neither secretary nor treasurer)

Now since the two events are mutually exclusive and Harry can neither be both secretary and treasurer, P(secretary and treasurer)=0.

P(Neither secretary nor treasurer)=(9/10)(8/9)(7/8).

What am I doing wrong?

If you want to do this way then: P(secretary or treasurer)=P(not Harry)*P(Harry)*P(any)+P(not Harry)*P(not Harry)*P(Harry)=9/10*1/9*1+9/10*8/9*1/8=2/10. In the red, you are calculating the probability that Harry will be secretary OR treasurer OR neither and we don't need neither.

Re: A certain club has 10 members, including Harry. One of the [#permalink]

Show Tags

16 Feb 2013, 12:58

5

This post received KUDOS

1

This post was BOOKMARKED

Favorable method:

Total options=10*9*8 // since any of the ten members can become President, any one of the nine can become secretary and any one of the remaining eight can become treasurer

Favorable options are the ones which include Harry as Treasurer or the secretary

Now consider the number of options in which harry is chosen as the secretary. Since we know that there is only one option for secretary, that position already has one person fixed. Hence, the president must be chosen out of the remaining nine people and the secretary from the remaining eight.

Hence, ways in which Harry can become secretary are 9*1*8=72

Similarly, ways in which Harry can become treasurer are 9*8*1=72

Since the probability asks for "or" we must add both the favorable outputs=72+72=144

Re: A certain club has 10 members, including Harry. One of the [#permalink]

Show Tags

18 Aug 2013, 13:59

Bunuel wrote:

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 be either the member chosen to 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

Diagnostic Test Question: 7 Page: 21 Difficulty: 650

President then Secretary or Treasurer

9/10 * 1/9 * 8/8 = 1/10 (when Harry is the secretary) or 9/10 * 8/9 * 1/8 = 1/10 (when Harry is the treasurer)

So probability = 1/10 + 1/10 = 1/5 (Answer E)
_________________

Re: A certain club has 10 members, including Harry. One of the [#permalink]

Show Tags

31 Oct 2014, 15:47

Hi Bunnel,

How can we just add 1/10+1/10, when the question clearly states "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"

I did it this way

9/10*1/9*8/8 + 9/10*8/9*1/8 = 1/10 + 1/10 = 1/5.

Just trying to understand the logic in your solution.

How can we just add 1/10+1/10, when the question clearly states "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"

I did it this way

9/10*1/9*8/8 + 9/10*8/9*1/8 = 1/10 + 1/10 = 1/5.

Just trying to understand the logic in your solution.

Cheers, Anie

Yes, we can that simply add 1/10 and 1/10.

What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer? So, what is the probability that Harry will be either 2nd or 3rd in the row? The probability of each is 1/10, so P = 1/10 + 1/10.

If you still have some doubts, please follow the links to the similar questions given above.

Re: A certain club has 10 members, including Harry. One of the [#permalink]

Show Tags

02 Nov 2014, 04:09

Bunuel wrote:

SOLUTION

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 be either the member chosen to 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.

So Bunuel you are saying that events are not defined, I mean to say that we can't assume that First president is selected, then Secretary and then Treasurer. Because if the events are imposed then the total number of available person will decrease in each event, because it is nowhere mentioned that one person can hold more than position. Please reply so that I can get rid of my doubts. Thanks!
_________________

Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

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 be either the member chosen to 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.

So Bunuel you are saying that events are not defined, I mean to say that we can't assume that First president is selected, then Secretary and then Treasurer. Because if the events are imposed then the total number of available person will decrease in each event, because it is nowhere mentioned that one person can hold more than position. Please reply so that I can get rid of my doubts. Thanks!

No. The sequence is the way it's given. But it does not matter, whether we select president first and secretary second or vise-versa.
_________________

Re: A certain club has 10 members, including Harry. One of the [#permalink]

Show Tags

26 Jan 2015, 04:56

1

This post received KUDOS

It wants to know the probability that Harry is Secretary or treasurer, so we should add the probability that he will be chosen secretary to the probability that he will be chosen treasurer.

The Probability that he is chosen secretary is 9/10*1/9*8/8=1/10

The 9/10 represents the probability that anyone but harry is president The 1/9 represents the probability that harry is secretary The 8/8 represents the fact that anyone can be treasurer, so it really does not affect the probability at all

The probability that he is chosen treasurer is 9/10*8/9*1/8=1/10

The 9/10 represents the probability that anyone but harry is president The 1/9 represents the probability anyone but harry is secretary The 1/8 represents the probability that harry is treasurer

Add the two together and you get 1/5 (E)
_________________

A certain club has 10 members, including Harry. One of the [#permalink]

Show Tags

26 Sep 2015, 13:12

1

This post received KUDOS

For an easy way to look at it and not be confused with how the probability can be 1/10 in each instance, think of it this way:

The question is asking the probability of either one or the other happening.

You have to find the probability that Harry will either be chosen as Secretary or treasurer.

Case 1 (Prob of Harry being chosen as Secretary)= Probability that anyone except Harry will be Selected as President (9/10) * Probability that Harry will be chosen as Secretary (1/9) * Probability that any of the others will be selected as treasurer (8/8)

Which is = 9/10 * 1/9 * 8/8 = 1/10

Case 2 (Probability that Harry will be selected as Treasurer) = Probability that anyone except Harry will be chosen as president (9/10) * Probability that anyone except Harry will be chosen as Secretary (8/9) * Probability that Harry will be chosen as Treasurer (8/8)

= 9/10 * 8/9 * 1/8 = 1/10

Now to find the answer, add the two probabilities (as we do in either or cases) to find the probability that Harry will either be chosen Secretary or Treasurer = 1/10 + 1/10 = 2/10 = 1/5

Answer: E

gmatclubot

A certain club has 10 members, including Harry. One of the
[#permalink]
26 Sep 2015, 13:12

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...