Board of directors

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chieftang: Master | Next Rank: 500 Posts; Posts: 218; Joined: Wed Nov 23, 2011 8:05 pmFollowed by: 4 members; Thanked: 26 times

by chieftang » Sun Dec 04, 2011 7:52 pm

Thought I'd throw this one up for you guys. Adapted from an OG question:

A board of directors has 10 members, including Gonzalo. Randomly, one of the 10 members is chosen to be the president, one of the remaining 9 members is randomly chosen to be the treasurer, and one of the remaining 8 members is randomly chosen to be the secretary. What is the probability that Gonzalo will be either the member chosen to be the secretary or the member chosen to be the treasurer?

(A) 1/720
(B) 1/20
(C) 1/10
(D) 1/9
(E) 1/5

OA to come.

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Source: Beat The GMAT — Problem Solving | Sun Dec 04, 2011 7:52 pm

user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Sun Dec 04, 2011 9:45 pm

[spoiler]IMO 1/5[/spoiler]

(9*1*8)/(10*9*8) + (9*8*1)/(10*9*8)

user123321

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Want to do it right the first time.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Dec 05, 2011 4:57 am

chieftang wrote:Thought I'd throw this one up for you guys. Adapted from an OG question:

A board of directors has 10 members, including Gonzalo. Randomly, one of the 10 members is chosen to be the president, one of the remaining 9 members is randomly chosen to be the treasurer, and one of the remaining 8 members is randomly chosen to be the secretary. What is the probability that Gonzalo will be either the member chosen to be the secretary or the member chosen to be the treasurer?

(A) 1/720
(B) 1/20
(C) 1/10
(D) 1/9
(E) 1/5

OA to come.

P(A or B) = P(A) + P(B).

Each of the 10 members has a 1/10 chance of being chosen secretary or treasury.
The intervening elections are IRRELEVANT.

P(Gonzales is chosen secretary or treasurer) = 1/10 + 1/10 = 1/5.

The correct answer is E.

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chieftang: Master | Next Rank: 500 Posts; Posts: 218; Joined: Wed Nov 23, 2011 8:05 pmFollowed by: 4 members; Thanked: 26 times

by chieftang » Mon Dec 05, 2011 7:45 am

GMATGuruNY wrote:
chieftang wrote:Thought I'd throw this one up for you guys. Adapted from an OG question:

A board of directors has 10 members, including Gonzalo. Randomly, one of the 10 members is chosen to be the president, one of the remaining 9 members is randomly chosen to be the treasurer, and one of the remaining 8 members is randomly chosen to be the secretary. What is the probability that Gonzalo will be either the member chosen to be the secretary or the member chosen to be the treasurer?

(A) 1/720
(B) 1/20
(C) 1/10
(D) 1/9
(E) 1/5

OA to come.
P(A or B) = P(A) + P(B).

Each of the 10 members has a 1/10 chance of being chosen secretary or treasury.
The intervening elections are IRRELEVANT.

P(Gonzales is chosen secretary or treasurer) = 1/10 + 1/10 = 1/5.

The correct answer is E.

Yes!!

And it bears out when you multiply the odds of NOT being chosen as president by the odds of being chosen as treasurer: (9/10)(1/9) = 1/10, and the odds of not being chosen as president, not being chosen as treasurer, and being chosen as secretary: (9/10)(8/9)(1/8) = 1/10

OA [spoiler]E[/spoiler]

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gunjan1208: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Jul 28, 2011 12:48 amFollowed by: 6 members; Thanked: 28 times

by gunjan1208 » Fri Dec 09, 2011 5:43 am

Hi,
I did it exactly the way described by Cheftang and got 1/10...

But the language does say that remaining 9...Remaining 8 etc....Therefore it needs to be done that way. What am I missing?

Guys, help.

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Sat Dec 10, 2011 11:40 am

chieftang wrote:Thought I'd throw this one up for you guys. Adapted from an OG question:

A board of directors has 10 members, including Gonzalo. Randomly, one of the 10 members is chosen to be the president, one of the remaining 9 members is randomly chosen to be the treasurer, and one of the remaining 8 members is randomly chosen to be the secretary. What is the probability that Gonzalo will be either the member chosen to be the secretary or the member chosen to be the treasurer?

(A) 1/720
(B) 1/20
(C) 1/10
(D) 1/9
(E) 1/5

OA to come.

Total no of ways = 10*9*8
No of possible selections
i) when Gonzalo is the treasurer = 9*1*8
ii) when he is the secr = 9*8*1
Total no of selections = 2*9*8

Probability = 2*9*8/10*9*8 = 1/5

Option E

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