BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Need help as I think there is an error in my book

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 73
Joined: Wed Jan 07, 2009 1:00 pm
Location: Tampa, FL
Thanked: 9 times
GMAT Score:630

Need help as I think there is an error in my book

by Mr2Bits » Wed Feb 18, 2009 11:20 am
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 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

I have worked this out but come up with a different answer than the books explanation and need help reasoning. I will post my answer and the books soon

:?:
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 258
Joined: Thu Aug 07, 2008 5:32 am
Thanked: 16 times

Re: Need help as I think there is an error in my book

by x2suresh » Wed Feb 18, 2009 11:33 am
Mr2Bits 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 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

I have worked this out but come up with a different answer than the books explanation and need help reasoning. I will post my answer and the books soon

:?:
ways for Harry be sec + ways for Harry to be treasurer
= 9C1*1C1*8C1 + 9C1*8C1*1C1

Total number of ways= 10C1*9C1*8C1


p= (9*8+9*8)/(10*9*8) = 2/10=1/5

E
Top
Senior | Next Rank: 100 Posts
Posts: 73
Joined: Wed Jan 07, 2009 1:00 pm
Location: Tampa, FL
Thanked: 9 times
GMAT Score:630

by Mr2Bits » Wed Feb 18, 2009 11:43 am
E is correct in the book but what I dont get is why they factor him being president in the combination of treasuerer and secretary. Once president is selected it's gone. You cannot elect the president again when the treasurer and secretary positions are being filled.

I came up with

9/10 * 1/9 *1/8 = 1/80 he makes either one.

9/10 being the chance of him not being president

1/9 being the chance he is secretary

1/8 being the chance he is treasurer

Each chance is not independant of the last is it not?
Top
Master | Next Rank: 500 Posts
Posts: 258
Joined: Thu Aug 07, 2008 5:32 am
Thanked: 16 times

by x2suresh » Wed Feb 18, 2009 11:55 am
Mr2Bits wrote:E is correct in the book but what I dont get is why they factor him being president in the combination of treasuerer and secretary. Once president is selected it's gone. You cannot elect the president again when the treasurer and secretary positions are being filled.

I came up with

9/10 * 1/9 *1/8 = 1/80 he makes either one.

9/10 being the chance of him not being president

1/9 being the chance he is secretary

1/8 being the chance he is treasurer

Each chance is not independant of the last is it not?

P(AUB) = P(A) + P(B) - P(A ∩ B)

P(A ∩ B) --> ZERO here.. because he can't be secretary and treasurer at the same time.


P(sec or tre)=P(AUB) = P(A) + P(B) = P(sec)+P(tre)
= 9/10*1/9*1/1 + 9/10*8/9*1/8 =2/10=1/5
Top
Master | Next Rank: 500 Posts
Posts: 431
Joined: Sat Jan 10, 2009 9:32 am
Thanked: 16 times
Followed by:1 members

1/5

by kanha81 » Wed Feb 18, 2009 12:19 pm
Here's how I solved the problem:

Let P(X=P)=1/10, X is someone who is not Harry, P is President
=> P(P')=1-1/10=9/10

lllly, P(H=S)=1/9, H is Harry, S is secretary
=> P(S')=1-1/9=8/9, S' is not Secretary

lllly, P(H=T)=1/8, T is Treasurer
=> P(T')=1-1/8=7/8, T' is not Treasurer

lllly, P(H=NonSelection)=1

Create a Table: Harry can be either Secretary or Treasurer, but not President

PRES SEC TRES
P' S T'
P' S' T

PRES SEC TRES
9/10 1/9 P(Non Selection)=1 (b/c Harry is already elected)
9/10 8/9 1/8

1st row: P(H=S) = (9/10) * (1/9) * 1 = 1/10
2nd row: P(H=T) = (9/10) * (8/9) * (1/8) = 1/10

P(H=S) + P(H=T) = 2(1/10) = 1/5

Hence, [E]
Want to Beat GMAT.
Always do what you're afraid to do. Whoooop GMAT
Top
Senior | Next Rank: 100 Posts
Posts: 73
Joined: Wed Jan 07, 2009 1:00 pm
Location: Tampa, FL
Thanked: 9 times
GMAT Score:630

by Mr2Bits » Wed Feb 18, 2009 12:55 pm
Thanks all, I get it now, I need to calulate them as two seperate events and not one. :lol:
Top
Post new topic Post Reply
• Page 1 of 1