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.
kim has 5 pairs of shoes; each pair is a different color...
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P(matching pair) = P(select ANY shoe for 1st selection AND select matching shoe for 2nd selection)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(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)
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Here's an approach that uses counting techniquesAAPL 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) = (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] https://www.gmatprepnow.com/module/gmat- ... /video/789
So, P(matching pair) = (5)/(45)
= 1/9
= C
Cheers,
Brent
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- Scott@TargetTestPrep
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The probability that Kim will select two shoes of the same color is: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
The OA is C.
2/10 x 1/9 x 5 = 1/45 x 5 = 1/9
Alternate solution:
Since the first shoe she picks does not matter, then the probability of picking the first shoe is 10/10 = 1. However, since only 1 shoe is left to match the color of that shoe, the probability of picking the second shoe matching the color of the first one is 1/9. Therefore, the probability that Kim will pick two shoes of the same color is 1 x 1/9 = 1/9.
Answer: C
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