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 February 3rd, 2014, 08:37 AM #1 Newbie   Joined: Feb 2014 Posts: 3 Thanks: 0 Probability! Help Needed! I'm taking a probability class and this question was posed by my teacher. it seems simple but me and my friend have been stuck on it for a while. Can anyone help answer this question or at least pose a method to answering it for us? You are rushing to go away for the weekend and you randomly grab 4 shoes from 4 different pairs in your closet. What is the probability that you have at least one pair?
 February 3rd, 2014, 09:15 AM #2 Senior Member     Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry Re: Probability! Help Needed! (1) FIrst fined total chances. C(16,4) (2) Then calculate One pair and non-pairs C(8,1)*C(14,1)*C(12,1) (3) Find chances for two pairs C(8,2) Answer is [(2) + (3)]/(1)
 February 3rd, 2014, 09:26 AM #3 Newbie   Joined: Feb 2014 Posts: 3 Thanks: 0 Re: Probability! Help Needed! but the answer has to be less than 1 if its the probability. we know the answer is roughly .77 or exactly 27/35, but we don't know how to get to that.
February 3rd, 2014, 12:46 PM   #4
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Re: Probability! Help Needed!

Quote:
 Originally Posted by shcorina I'm taking a probability class and this question was posed by my teacher. it seems simple but me and my friend have been stuck on it for a while. Can anyone help answer this question or at least pose a method to answering it for us? You are rushing to go away for the weekend and you randomly grab 4 shoes from 4 different pairs in your closet. What is the probability that you have at least one pair?
1/7(a) + (6/7)(2/6)(b) + (6/7)(4/6)(3/5)(c) = 27/35
a - prob. that second shoe is match
b - prob. that third shoe is match (second shoe not)
c - prob. that fourth shoe is match (second and third not)

match means match to any previously chosen.

February 3rd, 2014, 01:39 PM   #5
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Re: Probability! Help Needed!

Hello, shcorina!

Quote:
 You randomly grab 4 shoes from 4 different pairs in your closet. What is the probability that you have at least one pair?

$\text{There are 8 shoes: }\:\{A,A,\,B,B,\,C,C\,D,D\}$

$\text{You select 4 of them: }\:{8\choose4} \,=\,70\text{ possible outcomes.}$

$\text{What is the probability of getting }no\text{ matching pairs?}
\;\;\;\text{You must pick 4 different shoes: }\:\{A,B,C,D\}
\text{There are: }\:2\,\cdot\,2\,\cdot\,2\,\cdot\,2 \:=\:16\text{ ways to do this.}$

$\text{Hence: }\:P(\text{no pairs}) \:=\:\frac{16}{70} \:=\:\frac{8}{35}$

$\text{Therefore: }\:P(\text{at least one pair}) \:=\:1\,-\,\frac{8}{35} \:=\:\frac{27}{35}$

February 3rd, 2014, 05:02 PM   #6
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Re: Probability! Help Needed!

Quote:
 Originally Posted by shcorina You are rushing to go away for the weekend and you randomly grab 4 shoes from 4 different pairs in your closet. What is the probability that you have at least one pair?
Corina, what is probability if you grab 5 shoes? Careful....

 Tags needed, probability

### a closet contains 8 pairs of shoes. you pick out 5. what is the probability of a)no pair, b) exactly one pair, and c) two pairs?

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