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tricky probability

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by mariah » Wed Aug 25, 2010 10:51 am
There are five pairs of shoes with different colors in a box. If two shoes are to be selected from the box without replacement, what is the probability that they have the same color?

1/9
2/9
1/3
3/8
2/3

please come with explanations
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by RickH » Wed Aug 25, 2010 11:06 am
What's the correct answer?
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by Maciek » Wed Aug 25, 2010 11:30 am
Hi Mariah!

it is great question. Thank you for posting it.

IMO A

The formula for finding the probability of an event A:
P(A) = the number of ways event A can occur / the total number of possible outcomes

A - two shoes, that were selected from the box without replacement, have the same color
There are five pairs of shoes with different colors in a box


so 5 is the number of ways event A can occur

We find the the total number of possible outcomes with combination formula

combination formula
A formula for the number of possible combinations of r objects from a set of n objects.
Image

Please read the lesson:
https://www.beatthegmat.com/mba/2010/08/ ... -your-head

10C2 = 10*9/2 = 45

Let us plug in the numbers

P(A) = 5/45 = 1/9

I choose answer A.

hope it helps!
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by Ian Stewart » Wed Aug 25, 2010 12:33 pm
Or you can look at it this way: no matter what shoe you pick first, there are 9 shoes left, exactly 1 of which matches your first selection. So the probability of getting two matching shoes must be 1/9.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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