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probability that they are matching shoes?

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probability that they are matching shoes?

by uptowngirl92 » Wed Oct 28, 2009 12:09 am
A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
1/190

1/20

1/19

1/10

1/9


OA:C

Please see my method:
...................................................

Numerator:
Out of 20 shoes we have to select one shoe first..w/o any restrictions.So that's 20C1 (choosing one out of 20).
Now,the second show has to be the matching shoe.There is only ONE such possible shoe,so the probability of choosing that shoe is 1.

Denominator:
Chosing 2 shoes out of 20.So, 20C2

20C1/20C2 = 2/19

please explain:(
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Re: probability that they are matching shoes?

by xcusemeplz2009 » Wed Oct 28, 2009 3:15 am
uptowngirl92 wrote:A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
1/190

1/20

1/19

1/10

1/9


OA:C

Please see my method:
...................................................

Numerator:
Out of 20 shoes we have to select one shoe first..w/o any restrictions.So that's 20C1 (choosing one out of 20).
Now,the second show has to be the matching shoe.There is only ONE such possible shoe,so the probability of choosing that shoe is 1.

Denominator:
Chosing 2 shoes out of 20.So, 20C2

20C1/20C2 = 2/19

please explain:(
i am getting altogether a diff ans
my approah
desiarble cases=20*1

total cases=20*19

p=1/19

???
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by ssmiles08 » Wed Oct 28, 2009 4:16 am
Firstly, you are choosing two shoes out of 20. and 2 of them have be from the same pair.

2C2/20C2 = 1/190

next, you have 10 different pairs. So there are 10 more possible ways you can get a pair of shoes.

so it is 1/190 * 10 = 1/19 (C)
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by jaspreet_takhar » Wed Oct 28, 2009 4:17 am
I did a slightly different calculation.
probability of selecting the first shoe - 1
probaility of selecting the second shoe such that it forms a pair with the first one - 1/19

total probability - 1*1/19 = 1/19
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by mp2437 » Wed Oct 28, 2009 5:27 am
I did it the same way as jaspreet. Just try to understand what's going on.

You have 20 shoes, and are looking for a matching pair. The first shoe you take could be anyone, so probability of getting one shoe is 1. Now, you took 1 shoe out of the 20 original, and you have 19 left, but there is only 1 shoe in the 19 that matches the first one. So the probability to get the matching shoe is 1/19.

So multiply your probabilities: 1 * 1/19 = 1/19
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by crackthetest » Mon Nov 16, 2009 2:24 pm
here is the way of how I solved it

Right, Left - legs

you have 10 Rs and 10 Ls

Prob of choosing R out of 20, then matching pair L from rest : 10/20 * 1/19 = 1/38.

similarly you can choose L first then R, hence 1/38 * 2 = 1/19.
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by Ian Stewart » Mon Nov 16, 2009 5:49 pm
uptowngirl92 wrote: Numerator:
Out of 20 shoes we have to select one shoe first..w/o any restrictions.So that's 20C1 (choosing one out of 20).
Now,the second show has to be the matching shoe.There is only ONE such possible shoe,so the probability of choosing that shoe is 1.

Denominator:
Chosing 2 shoes out of 20.So, 20C2

20C1/20C2 = 2/19

please explain:(
Jaspreet's solution above is the one I use for similar problems - it's very fast. Still, it's perfectly possible to solve as you've done above, provided you are consistent in how you count the numerator and denominator. In your solution above, when you count the number of selections for the numerator, you are assuming that order matters (you have a 'first shoe' and a 'second shoe'), but when you count the number of selections for the denominator, you are assuming that order does *not* matter - 20C2 means 'the number of ways to choose 2 things from 20 if the order is *not* important'.

It doesn't matter which perspective you take - you can think of selecting a first shoe, then a second, so order matters, or you can think of selecting both shoes at once, so order doesn't matter, but you must be absolutely sure you count the numerator and denominator in the same way: if you assume order matters when working out the numerator, you must assume it matters when you work out the denominator. So, if you assume order matters, you get, as you found above, 20 for the numerator, and 20*19 for the denominator (20 choices for the first shoe, 19 for the second). If you assume order does not matter, then there are 10 pairs we could choose that give the result we want, and 20C2 ways to choose two shoes. In either case, if you divide you'll get the answer: 20/(20*19) = 10/20C2 = 1/19.
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by samirnajeeb » Tue Feb 08, 2011 6:44 am

20/20 * 1/19 = 1/19

for the first shoe, you can take any out of 20. so probability = 20/20
haven chosen the shoe, we are left with only 1 matching shoe out of the remaining 19, so probability = 1/19

hth.
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