Emily keeps 12 different pairs of shoes (24 individual shoes in total)

Question

Emily keeps 12 different pairs of shoes (24 individual shoes in total) under her bed. If her dog drags out two shoes at random, what is the probability that he drags out a matching pair of shoes?

A. 1/144
B. 1/66
C. 1/23
D. 1/12
E. 1/11

u1983 · Answer

No of ways selecting the 1st shoe = 24 
No of ways selecting the 1st & 2nd shoe= 24 *23
No of ways selecting the 2nd shoe which is the exact pair of the 1st = 1
No of ways selecting selecting the 1st shoe & the 2nd shoe which is the exact pair of the 1st= 24*1
Hence P = 24*1 /24*23 = 1/23 .......   Ans C

iamzyw · Answer

Probability of the first one don't not matter, so we should consider what is the probability of the second one be the pair of the first one.

1/23

Answer C

honneeey · Answer

Hi,

My approach-

Probability of selecting a particular shoe from the 12 different pair=2/24
Now probability of selecting the matching shoe to the shoe already dragged= 1/23(remember one shoe is already out)

Therefore combined probability of one matching pair of shoe= 1/24* 1/23

Now, there are 12 different pair of shoe so your probability will shoot up 12 times-

2/24 *1/23 *12=1/23.

Bunuel is it correct?

ScottTargetTestPrep · Answer

The first shoe can be any shoe, so its probability is 24/24 = 1. However, since the second shoe must match the first shoe, its probability of being chosen is 1/23. Therefore, the probability of the two shoes forming a matching pair is 1 x 1/23 = 1/23.

Answer: C

BrentGMATPrepNow · Answer

P(dog selects matching pair) = P(dog chooses ANY sock 1st   AND   2nd sock matches the 1st sock)
= P(dog chooses ANY sock 1st)   x   P(2nd sock matches the 1st sock)
= 24/24   x   1/23
= 1/23

Answer: C

Cheers,
Brent

fskilnik · Answer

\left. \matrix{
 {\rm{Total}}\,\,:\,\,\,C\left( {24,2} \right) = {{24 \cdot 23} \over 2} = 12 \cdot 23\,\,{\rm{equiprobable}}\,\,{\rm{pairs}}\,\,\,\, \hfill \cr 
 {\rm{Favorable:}}\,\,\,12\,\,{\rm{real}}\,\,{\rm{pairs}}\,\,\left( {{\rm{matches}}} \right) \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = {{12} \over {12 \cdot 23}} = {1 \over {23}}

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

GMATinsight · Answer

Method 1:

Probability = Favourable outcomes / Total outcomes = Total Pairs / Total ways of picking 2 shoes out of 24

i.e. Required probability  = \frac{12C1}{24C2} = \frac{12}{(12*23)} = \frac{1}{23}

Answer: Option C

Method 2:

Probability = Favourable outcomes / Total outcomes = Total ways of picking two shoes making pair / Total ways of picking 2 shoes out of 24

i.e. Required probability  = \frac{(24*1)}{(24*23)}

Favourable outcomes:  first shoe may be picked in 24 ways but second shoe may be picked only in one way to make pair of shoe
 Total outcomes:  first shoe may be picked in 24 ways and second shoe may be picked in 23 ways

Answer: Option C

ScottTargetTestPrep · Answer

The probability that the dog will drag out any matching pair is:

2/24 x 1/23 = 1/12 x 1/23

Since there are 12 different pairs, the total probability is 12 x (1/12 x 1/23) = 1/23.

Alternate Solution:

The dog can drag any shoe out, leaving 23 shoes under the bed. The probability that the next shoe he drags out is its match is 1/23.

Answer: C

SchruteDwight · Answer

Ways to select first = 24
Ways to select second = 1
But since the order is irrelevant, there are really just 12 ways
Total ways to choose 2 from 24 (order irrelevant) = 24C2

hence 12/24C2

SchruteDwight · Answer

why do you not have to divide both (24*1) and (24*23) by 2? Or did you just leave that out?

GMATinsight · Answer

ghnlrug

In probability calculation, you must calculate both numerator and denominator either by selection (Method 1) or by Arrangement (Method 2) so in either case, you get the correct answer therefore dividing by 2 wasn't needed.

Kinshook · Answer

Probability = 11*1/24*23 = 1/23

IMO C

Posted from my mobile device

Basshead · Answer

Probability of selecting a shoe = 1
Probability of selecting a 2nd shoe that matches the first shoe: 1/23

1 * (1/23) = 1/23

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Emily keeps 12 different pairs of shoes (24 individual shoes in total)

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