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# Jessica's laundry basket contains 15 different pairs of socks. If she

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Math Expert
Joined: 02 Sep 2009
Posts: 55635
Jessica's laundry basket contains 15 different pairs of socks. If she  [#permalink]

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07 Aug 2018, 03:59
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:10) correct 21% (01:30) wrong based on 113 sessions

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Jessica's laundry basket contains 15 different pairs of socks. If she reaches in to the basket and pulls two socks at random, what is the probability that she pulls out a matching pair?

A. 1/900
B. 1/870
C. 1/210
D. 1/29
E. 1/28

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Joined: 22 Feb 2018
Posts: 428
Re: Jessica's laundry basket contains 15 different pairs of socks. If she  [#permalink]

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07 Aug 2018, 04:37
2
1
OA: D

Total socks $$: 2*15 = 30$$
1st Pick : Probability of picking any one sock out of $$30$$ socks =$$\frac{30}{30}$$
2nd Pick : Probability of picking another sock of same pair as picked in 1st Pick =$$\frac{1}{29}$$
Final probability $$: \frac{30}{30} * \frac{1}{29}=\frac{1}{29}$$
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##### General Discussion
Director
Joined: 20 Feb 2015
Posts: 791
Concentration: Strategy, General Management
Re: Jessica's laundry basket contains 15 different pairs of socks. If she  [#permalink]

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07 Aug 2018, 12:49
1
Bunuel wrote:
Jessica's laundry basket contains 15 different pairs of socks. If she reaches in to the basket and pulls two socks at random, what is the probability that she pulls out a matching pair?

A. 1/900
B. 1/870
C. 1/210
D. 1/29
E. 1/28

number of ways she can pull two socks of the same colour = 15 ways
no of ways she can pull two socks of any colour = 30c2
probability= 15/30c2 = 15/15*29=1/29
Director
Joined: 27 May 2012
Posts: 801
Jessica's laundry basket contains 15 different pairs of socks. If she  [#permalink]

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10 Sep 2018, 06:18
CounterSniper wrote:
Bunuel wrote:
Jessica's laundry basket contains 15 different pairs of socks. If she reaches in to the basket and pulls two socks at random, what is the probability that she pulls out a matching pair?

A. 1/900
B. 1/870
C. 1/210
D. 1/29
E. 1/28

number of ways she can pull two socks of the same colour = 15 ways
no of ways she can pull two socks of any colour = 30c2
probability= 15/30c2 = 15/15*29=1/29

Hi CounterSniper

You have used two different techniques for solving almost the same question,and arrived at different answers could you care to explain both questions using the same method?

https://gmatclub.com/forum/5-pairs-of-s ... 74309.html

Actually answer should be 2/9 for the question in the link above , but sadly that is not among the options.
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- Stne
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Joined: 20 Feb 2015
Posts: 791
Concentration: Strategy, General Management
Jessica's laundry basket contains 15 different pairs of socks. If she  [#permalink]

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10 Sep 2018, 06:43
stne wrote:
CounterSniper wrote:
Bunuel wrote:
Jessica's laundry basket contains 15 different pairs of socks. If she reaches in to the basket and pulls two socks at random, what is the probability that she pulls out a matching pair?

A. 1/900
B. 1/870
C. 1/210
D. 1/29
E. 1/28

number of ways she can pull two socks of the same colour = 15 ways
no of ways she can pull two socks of any colour = 30c2
probability= 15/30c2 = 15/15*29=1/29

Hi CounterSniper

You have used two different techniques for solving almost the same question,and arrived at different answers could you care to explain both questions using the same method?

https://gmatclub.com/forum/5-pairs-of-s ... 74309.html

Actually answer should be 2/9 for the question in the link above , but sadly that is not among the options.

Hi stne
consider below

the first sock can be picked in 30 ways (we have a total of 30 socks)
the second one can be picked in only one way (why ? because we have already picked a sock of a given pair and we have to pick the same one the second time)

p(first sock) = 30/30=1
p(second sock) = 1/29

required probability = 1/29

I have also posted an explanation on the thread you have mentioned above
Jessica's laundry basket contains 15 different pairs of socks. If she   [#permalink] 10 Sep 2018, 06:43
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