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## #1 2012-12-28 13:27:50

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Probability problem

Hi, please, tell me if my was of solving this problem is good or not : Users of public transport are waiting for the bus: 3 women and 1 man. One of them wears glasses, another gloves, and another a hat. What is the probability that the man has none of these accessories?

Here how :

1:Woman
2:Woman
3:Woman
4:Man
Glasses, Gloves, Hat, Nothing

All possible combinations :

{1,2,3,4} {1,2,4,3} {1,3,2,4} {1,3,4,2} {1,4,2,3} {1,4,3,2} {2,1,3,4} {2,1,4,3} {2,3,1,4} {2,3,4,1} {2,4,1,3} {2,4,3,1} {3,1,2,4} {3,1,4,2} {3,2,1,4} {3,2,4,1} {3,4,1,2} {3,4,2,1} {4,1,2,3} {4,1,3,2} {4,2,1,3} {4,2,3,1} {4,3,1,2} {4,3,2,1}

Probability of the man having nothing : 6/24 or 0,25

___________________________________________________

Now here's what the ''real'' answer is : 54/72 or 0,75

I figured that they could have obtained this answer by multiplying 18/24 X3 = 54/72 (In my opinion, this is an error because the question is what is the probability that the man has NONE of these accesories and 18/24 is the probability that he wears one of these objects! Am I correct?) So the ''real'' answer would be 18/72

And last thing that bugs me, if I'm correct in all my previous statements, why is the answer on 72 ? There is 24 possibilities ! Why multiply by 3 ? Does the order of the object change anything ? (WHich isn't logical, if you ask me)

Thank you

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## #2 2012-12-28 13:41:11

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Probability problem

I think you are correct and the problem meant to say what is the probabil that the man has one (not none) of these accessori, in which case 3/4 would be he is wearing one of the things.  Your iteration of the permutations seems correct.  I would stick to your guns. Good Luck.

igloo myrtilles fourmis

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## #3 2012-12-28 13:44:33

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

### Re: Probability problem

Ok, thanks for the fast answer ! And do you have any idea why the answer would be 18/72 (which before was 54/72) and not 6/24 ? Why multiply it by 3 ? Logicaly, the order of the items shouldn't change anything ... ???

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## #4 2012-12-29 05:29:14

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

up !

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## #5 2012-12-29 07:17:41

muxdemux
Member
Registered: 2012-12-23
Posts: 80

### Re: Probability problem

I agree with John.

You're right that the order doesn't change anything in this question. I'm not really sure why they multiplied it by 3, myself -- though your answer is correct and you seem to understand how to solve these kinds of problems, so I wouldn't worry about it.

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## #6 2012-12-29 07:28:48

Al-Allo
Member
Registered: 2012-08-23
Posts: 324

ok, thanks !

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