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A girl has 5 pairs of shoes, each pair being a different style. If she

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Bunuel
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A girl has 5 pairs of shoes, each pair being a different style. If she [#permalink] New post   23 Feb 2021, 10:00
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A girl has 5 pairs of shoes, each pair being a different style. If she selects 2 shoes at random, what is the probability they form a matching pair ?

A. 1/20
B. 1/10
C. 1/9
D. 1/5
E. 2/5
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C
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BrentGMATPrepNow
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Re: A girl has 5 pairs of shoes, each pair being a different style. If she [#permalink] New post   23 Feb 2021, 11:34
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Bunuel wrote:
A girl has 5 pairs of shoes, each pair being a different style. If she selects 2 shoes at random, what is the probability they form a matching pair ?

A. 1/20
B. 1/10
C. 1/9
D. 1/5
E. 2/5


P(matching pair) = P(1st shoe is ANY shoe AND 2nd shoe matches the 1st selection)
= P(1st shoe is ANY shoe) x P(2nd shoe matches the 1st selection)
= 10/10 x 1/9
= 1/9

Answer: C
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Re: A girl has 5 pairs of shoes, each pair being a different style. If she [#permalink] New post   26 Feb 2021, 21:36
P(any shoe) * P (matching shoe from the remaining)
10/10 * 1/9

ps - without replacement is implied, since the shoes are limited
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Re: A girl has 5 pairs of shoes, each pair being a different style. If she [#permalink] New post   27 Feb 2021, 07:47
there are 45 possible combinations inasmuch: 10!/2!*8! =45
now we have at most 5 possible combintions of selecting 5 same pairs of shoes
5/45= 1/9
ANSWER C
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Re: A girl has 5 pairs of shoes, each pair being a different style. If she [#permalink] New post   28 Feb 2021, 08:04
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Given
    • A girl has 5 pairs of shoes.
    • Each pair has a different style.
    • Girls selects 2 shoes at random

To find

    • The probability both the shoes are from a pair

Approach
    • Probability both the shoes are from a pair = \(\frac{Total\ case\ of\ picking\ a\ pair\ of\ shoe }{ Total\ cases\ of\ picking\ 2\ shoes}\)
      o Total case of picking a pair of shoe = 5 Pairs of shoes = 5 ways
      o Total cases of picking 2 shoes = 10 C2 = 45
    • Probability both the shoes are from a pair = \(\frac{5 }{ 45}\) = \(\frac{1}{9}\)
Hence, the correct answer is option C.
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Re: A girl has 5 pairs of shoes, each pair being a different style. If she [#permalink] New post   28 Feb 2021, 08:14
Total number of combinations possible - 10C2 = 45
Probability = 5 pairs/ 45 pairs = 1/9

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Re: A girl has 5 pairs of shoes, each pair being a different style. If she [#permalink] New post   12 Mar 2021, 15:17
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Bunuel wrote:
A girl has 5 pairs of shoes, each pair being a different style. If she selects 2 shoes at random, what is the probability they form a matching pair ?

A. 1/20
B. 1/10
C. 1/9
D. 1/5
E. 2/5


Solution:

There are 10 shoes. The first shoe can be any shoe; however, since there is only 1 shoe of the 9 remaining shoes that can match the first shoe, the probability of obtaining a matching pair is 1/9.

Answer: C
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Re: A girl has 5 pairs of shoes, each pair being a different style. If she [#permalink]
12 Mar 2021, 15:17
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