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A man chooses an outfit from 3 different shirts, 2 different [#permalink]
 28 Nov 2007, 03:59
Question Stats:
50% (04:45) correct
50% (02:39) wrong based on 0 sessions
A man chooses an outfit from 3 different shirts, 2 different pairs of shoes, and 3 different pants. If he randomly selects 1 shirt, 1 pair of shoes, and 1 pair of pants each morning for 3 days, what is the probability that he wears the same pair of shoes each day, but that no other piece of clothing is repeated?
a) (1/3)^6 (1/2)^3
b) (1/3)^6 (1/2)
c) (1/3)^4
d) (1/3)^2 (1/2)
e) 5(1/3)^2
Would somone provide an explanation when giving your answer cause I didn't know how to solve this.
thanks
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Manager
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I don't know if I'm right, but this is how I approached it:
Shirts Shoes Pants
Day 1 3/3 2/2 3/3
(It doesn't matter what he chooses on day 1)
Day 2 2/3 1/2 2/3
(On day 2 he can't choose the shirt or pants he had on Day 1, so there's a 2/3 chance of getting each of those right. And he has to choose the same shoes, a 1/2 chance)
Day 3 1/3 1/2 1/3
(On day 3 he can't choose the shirt or pants he had on Day 1 or 2, so there's a 1/3 chance of getting each of those right. And he has to choose the same shoes, a 1/2 chance)
Multiply all probabilities and you get 1*2/9*1/18 = 1/81 or 1/3^4
Answer:(C)
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SVP
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i sort of approached it the same way as above, but instead of having 2/3 for shirt and pants on day 2, i had 1/2
my logic was on day 2 he only has 2 shirts and 2 pants to pick from, and he picks one .... i didnt end up with any of those answer choices though 
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the OA is C, however, I don't even know how to approach this, so while i'm trying to figure this out, you guys can also think of the appropriate steps in approaching it. anyone managed to figure it out? Although Raffie got the correct answer, i'm really not too sure of the steps that you have taken. or is it appropriate?
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CEO
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C.
we have
t=(2/2*1/2*1/2) - for shoes.
q=(3/3*2/3*1/3) - for shirts and the same fore pants.
P=t*q*q=(2/2*1/2*1/2)*(3/3*2/3*1/3)*(3/3*2/3*1/3)=1/4*4/3^4=(1/3)^4
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CEO
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walker wrote: C.
we have
t=(2/2*1/2*1/2) - for shoes.
q=(3/3*2/3*1/3) - for shirts and the same fore pants.
P=t*q*q=(2/2*1/2*1/2)*(3/3*2/3*1/3)*(3/3*2/3*1/3)=1/4*4/3^4=(1/3)^4
Aha. Very nice!!!
I forgot about the 1/3 on the last day! I kept making it 2/3. Makes so much sense now!
Set it up exactly as you did cept for the 1/3, which made all the difference!
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SVP
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had to come back to this one and ask:
why is probability on day2 for pants and shirts 2/3 ?
if we are told that these items cannot repeat, then since one item was already selected on day 1, doesnt that only leave 2 items for him to choose from on day2 ?
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CEO
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pmenon wrote: had to come back to this one and ask:
why is probability on day2 for pants and shirts 2/3 ?
if we are told that these items cannot repeat, then since one item was already selected on day 1, doesnt that only leave 2 items for him to choose from on day2 ?
You are right in the case without replacement. But "he wears the same pair of shoes each day" means replacement for shoes. So we can assume that there also is replacement for pants and shirts and he can wear of 3 items of pants and shirts on 2nd an 3rd day.
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Thanks, walker ! I guess I had overlooked that .
Yes absolutely, if there is replacement, there are always 3 choices to select from for pants and shirt. Good call !
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Manager
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P (3 different shirts) = 1*2/3*1/3
P (same shoes) = 1/2*1/2
P (3 different pants) = 1*2/3*1/3
(1/9)^2 = (1/3)^4
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Director
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Re: PS: Probability [#permalink]
26 Aug 2008, 23:30
Total number fo ways = (3*2*3) = 18 Day one: 3*2*3/18 = 1 Day two: 2*1*2/18 = 4/18 Day three: 1/18 = 1/18 It is important to nore that we multply the probabilties of all three days, in order to get the total probability because selection of same things on different days from the same set makes the events as dependent events. Please see the attached picture for more clarity. (2*3^2)*(2^2)*(1)/(3^6*2^3) = [(2^3)*(3^2)]/[(2^3)*(3^6)] = (1/3)^4
Attachments
File comment: Probability
Probability.PNG [ 40.59 KiB | Viewed 2044 times ]
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Manager
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Re: PS: Probability [#permalink]
27 Aug 2008, 14:30
Day#1 Day#2 Day#3
Shirts: 3 x 2 x 1
Pants: 3 x 2 x 1
Shoes: 2 x 1 x 1
Total probable outcomes = 6 * 6 * 2 = 72
Total possible outcomes = 2^3 * 3^3 * 3^3
Therefore, Prob. = 72/2^3*3^3*3^3 =1/3^4
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Re: PS: Probability
[#permalink]
27 Aug 2008, 14:30
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