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kim has 5 pairs of shoes; each pair is a different color...

This topic has 2 expert replies and 0 member replies

kim has 5 pairs of shoes; each pair is a different color...

Post Thu Dec 07, 2017 10:05 am
Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly select 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color?

(A) 2/5
(B) 1/5
(C) 1/9
(D) 1/10
(E) 1/25

The OA is C.

I don't understand why that is the correct answer, I'm a little bit confused.

The first time that she select any shoes, the probability should be 2/10? I'm confused. Then in the second time that she select any shoes the probability should be 1/9? I'm not sure.

Experts, I need your help with this PS question. Thanks.

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GMAT/MBA Expert

Post Thu Dec 07, 2017 10:10 am
AAPL wrote:
Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly select 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color?

(A) 2/5
(B) 1/5
(C) 1/9
(D) 1/10
(E) 1/25
P(matching pair) = P(select ANY shoe for 1st selection AND select matching shoe for 2nd selection)
= P(select ANY shoe for 1st selection) x P(select matching shoe for 2nd selection)
= 1 x 1/9
= 1/9
= C

ASIDE: Once we have selected ANY shoe as the 1st selection, there are 9 shoes remaining. Of those 9 remaining shoes, only 1 matches the first shoe (thus the 1/9)

Cheers,
Brent

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GMAT/MBA Expert

Post Thu Dec 07, 2017 10:17 am
AAPL wrote:
Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly select 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color?

(A) 2/5
(B) 1/5
(C) 1/9
(D) 1/10
(E) 1/25
Here's an approach that uses counting techniques

P(matching pair) = (number of ways to get a matching pair)/(TOTAL number of ways to select 2 shoes)

number of ways to get a matching pair
There are 5 different colors.
So, there are 5 different ways to get a matching pair

TOTAL number of ways to select 2 shoes
There are 10 shoes altogether.
Since the order in which we select the 2 shoes does not matter, we can use combinations.
We can select 2 shoes from 10 shoes in 10C2 ways
10C2 = 45

Aside: If anyone is interested, we have a video on calculating combinations (like 10C2) in your head: [url] http://www.gmatprepnow.com/module/gmat-counting/video/789

So, P(matching pair) = (5)/(45)
= 1/9
= C

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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