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Two trade associations, A and B are holding a joint cocktail

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Two trade associations, A and B are holding a joint cocktail [#permalink] New post 17 Oct 2005, 12:53
Two trade associations, A and B are holding a joint cocktail party at a hotel ballroom. There are a total of 50 members and one half of the members belong to trade association A. If 10 members belong to both trade associations, then what is the probability of picking a member from this cocktail party that belongs only to trade association B?

a) ½
b) ¼
c) 3/10
d) 3/8
e) 5/8

OA is D

50 members total in BOTH associations

10 Members are members of both associations

1/2 members are in A thus 25 and 1/2 members in B thus 25

So you have 15 only in A and 15 only in B and 10 in both

Thus you have 40 PEOPLE total

15/40 = 3/8 = OA

nice try all! :twisted:

Last edited by Titleist on 17 Oct 2005, 13:10, edited 1 time in total.
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 [#permalink] New post 17 Oct 2005, 12:58
Answer is A

Association A & B = 10

Only Asso A = Total members of A + Both A & B
= 25 - 10 = 15

Hence Only Asso. B = 25

Probability = Only B / Total = 25/50 = 1/2
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 [#permalink] New post 17 Oct 2005, 13:00
A + B - A&B = 50
25 + B - 10 = 50
B = 35

We need (B- A&B)/50 = 25/50 = 1/2 (A)
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 [#permalink] New post 17 Oct 2005, 13:02
hmm

there are 50 memebers in all...half (25 are members of A) now of these 10 are members of both (A & B) then that means 15 are members of just A.

now if 10 are memebers of both then B has 15 members also who are just members of B

probability = 15/50=3/10
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 [#permalink] New post 17 Oct 2005, 13:07
A)
Its like a set theory problem...

A + B - (A&B) = 50
25 + B - 10 = 50
B=35
=> Only B = 35-10 = 25
Hence P(B) = 1/2
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 [#permalink] New post 17 Oct 2005, 13:11
OA=D see above for official explanation
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Re: Word Problem - Probability [#permalink] New post 17 Oct 2005, 13:18
Titleist wrote:
1/2 members are in A thus 25 and 1/2 members in B thus 25


Then, how would it satisfy this -
A + B - A&B = 50

25 + 25 - A&B = 50 -> A&B = 0??
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 [#permalink] New post 17 Oct 2005, 13:19
Titleist wrote:
OA=D see above for official explanation


Ah... classical mistake... I confused "total members" with "total people"!!
Nice one.

What was I smoking today!! :wall
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Re: Word Problem - Probability [#permalink] New post 17 Oct 2005, 13:20
gsr wrote:
Titleist wrote:
1/2 members are in A thus 25 and 1/2 members in B thus 25


Then, how would it satisfy this -
A + B - A&B = 50

25 + 25 - A&B = 50 -> A&B = 0??


Easy

25+25-10=40

Clear?
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 [#permalink] New post 17 Oct 2005, 13:23
Not clear! :?

"There are a total of 50 members" How can it be 25+25-10=40
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 [#permalink] New post 17 Oct 2005, 13:28
gsr wrote:
Not clear! :?

"There are a total of 50 members" How can it be 25+25-10=40


because your mistaking total PEOPLE with total MEMBERS


The 50 MEMBERS which Not so Obviously include an overcount of 10 Members who are in BOTH trade associations. Thus there are a total 40 PEOPLE.

50 members total
40 people total
10 people who are members of both a & b


1/2 of the members are in A = 25

1/2 of members in B = 25

Members who are in A&B = 10

25+25-10=40

getting to the 40 people part was the trickiest
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 [#permalink] New post 17 Oct 2005, 13:30
gsr wrote:
Not clear! :?

"There are a total of 50 members" How can it be 25+25-10=40


gsr: Total members - treat that as total "memberships" at each clubs... not total "heads" or "people".

Hope the attached diagram helps.

I made the same mistake!!
Attachments

peeps.gif
peeps.gif [ 2.58 KiB | Viewed 454 times ]


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 [#permalink] New post 17 Oct 2005, 13:41
Yes I see now what you guys are saying!

Ok. This is my strategy for today, every problem I get wrong, I am going to think of it as a 750+ problem and just move on! :nopem

Else :stupid :beat
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 [#permalink] New post 17 Oct 2005, 13:44
:saw

yup thats what you just did to my confidence level....LOL
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 [#permalink] New post 17 Oct 2005, 13:50
fresinha12 wrote:
:saw

yup thats what you just did to my confidence level....LOL


Ohh...fresinha12.. that's too harsh!!!
Remember you need to take proper care of yourself atleast till next week!! :nopem :cool
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 [#permalink] New post 17 Oct 2005, 13:59
fresinha12 wrote:
:saw

yup thats what you just did to my confidence level....LOL


That which does not kill us makes us stronger.
-Friedrich Nietzsche

:beatup
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 [#permalink] New post 17 Oct 2005, 14:00
vikramm wrote:
gsr wrote:
Not clear! :?

"There are a total of 50 members" How can it be 25+25-10=40


gsr: Total members - treat that as total "memberships" at each clubs... not total "heads" or "people".

Hope the attached diagram helps.

I made the same mistake!!


great diagram vikram! :wink:
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 [#permalink] New post 18 Oct 2005, 01:10
I still think the stem is confusing, "If 10 members belong to both trade associations" implies member = person. It should read: "if two people belong to both trade associations".
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 [#permalink] New post 18 Oct 2005, 01:39
Total number of members = 15*2 + 10 = 40
Probability = 15/40 = 3/8 (D)
  [#permalink] 18 Oct 2005, 01:39
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