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Director
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Two trade associations, A and B are holding a joint cocktail [#permalink]
 17 Oct 2005, 13:53
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! 
Last edited by Titleist on 17 Oct 2005, 14:10, edited 1 time in total.
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Senior Manager
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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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Director
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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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Current Student
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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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Senior Manager
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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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Director
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OA=D see above for official explanation
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Director
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Re: Word Problem - Probability [#permalink]
17 Oct 2005, 14:18
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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Senior Manager
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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!! 
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Re: Word Problem - Probability [#permalink]
17 Oct 2005, 14:20
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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Director
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Not clear! 
"There are a total of 50 members" How can it be 25+25-10= 40
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Director
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gsr wrote: Not clear! "There are a total of 50 members" How can it be 25+25-10= 40because 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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Senior Manager
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gsr wrote: Not clear! "There are a total of 50 members" How can it be 25+25-10= 40gsr: 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 [ 2.58 KiB | Viewed 276 times ]
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Director
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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! 
Else  
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yup thats what you just did to my confidence level....LOL
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Director
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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!! 
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Director
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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
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Director
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vikramm wrote: gsr wrote: Not clear! "There are a total of 50 members" How can it be 25+25-10= 40gsr: 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! 
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Manager
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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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Total number of members = 15*2 + 10 = 40
Probability = 15/40 = 3/8 (D)
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