Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yell [#permalink]

Show Tags

27 May 2010, 03:41

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

54% (02:32) correct
46% (01:50) wrong based on 7 sessions

HideShow timer Statistics

There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yellow, 2 green. You select randomly four socks together. What is the probability that you'll get at least two of the same color?

There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yellow, 2 green. You select randomly four socks together. What is the probability that you'll get at least two of the same color?

"Probability that you'll get at least two of the same color" - means at least one pair (one pair or two pairs out of 4 socks).

P(at least one pair)=1-P(no pair) --> no pair means all socks must be of different colors --> \(P=1-\frac{C^4_5*2^4}{C^4_{10}}=\frac{13}{21}\).

\(C^4_5\) - # of ways to choose 4 different colors out of 5, basically # of ways to choose which 4 color socks will give us one sock (in this case we obviously will have 4 different colors); \(2^4\) - each of 4 chosen colors can give left or right sock; \(C^4_{10}\) - total # of ways to choose 4 socks out of 10.

What solution was given in the book for 41/42? _________________

There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yellow, 2 green. You select randomly four socks together. What is the probability that you'll get at least two of the same color?

"Probability that you'll get at least two of the same color" - means at least one pair (one pair or two pairs out of 4 socks).

P(at least one pair)=1-P(no pair) --> no pair means all socks must be of different colors --> \(P=1-\frac{C^4_5*2^4}{C^4_10}=\frac{13}{21}\).

\(C^4_5\) - # of ways to choose 4 different colors out of 5, basically # of ways to choose which 4 color socks will give us one sock (in this case we obviously will have 4 different colors); \(2^4\) - each of 4 chosen colors can give left or right sock; \(C^4_{10}\) - total # of ways to choose 4 socks out of 10.

There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yellow, 2 green. You select randomly four socks together. What is the probability that you'll get at least two of the same color?

"Probability that you'll get at least two of the same color" - means at least one pair (one pair or two pairs out of 4 socks).

P(at least one pair)=1-P(no pair) --> no pair means all socks must be of different colors --> \(P=1-\frac{C^4_5*2^4}{C^4_10}=\frac{13}{21}\).

\(C^4_5\) - # of ways to choose 4 different colors out of 5, basically # of ways to choose which 4 color socks will give us one sock (in this case we obviously will have 4 different colors); \(2^4\) - each of 4 chosen colors can give left or right sock; \(C^4_{10}\) - total # of ways to choose 4 socks out of 10.

What solution was given in the book for 41/42?

wait a sec i dont get it. Why isnt 5 choose 4 \(C^5_4\) ? _________________

There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yellow, 2 green. You select randomly four socks together. What is the probability that you'll get at least two of the same color?

"Probability that you'll get at least two of the same color" - means at least one pair (one pair or two pairs out of 4 socks).

P(at least one pair)=1-P(no pair) --> no pair means all socks must be of different colors --> \(P=1-\frac{C^4_5*2^4}{C^4_10}=\frac{13}{21}\).

\(C^4_5\) - # of ways to choose 4 different colors out of 5, basically # of ways to choose which 4 color socks will give us one sock (in this case we obviously will have 4 different colors); \(2^4\) - each of 4 chosen colors can give left or right sock; \(C^4_{10}\) - total # of ways to choose 4 socks out of 10.

What solution was given in the book for 41/42?

May i knw the logic behind this? m not getting the numerator part .. _________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yellow, 2 green. You select randomly four socks together. What is the probability that you'll get at least two of the same color?

"Probability that you'll get at least two of the same color" - means at least one pair (one pair or two pairs out of 4 socks).

P(at least one pair)=1-P(no pair) --> no pair means all socks must be of different colors --> \(P=1-\frac{C^4_5*2^4}{C^4_10}=\frac{13}{21}\).

\(C^4_5\) - # of ways to choose 4 different colors out of 5, basically # of ways to choose which 4 color socks will give us one sock (in this case we obviously will have 4 different colors); \(2^4\) - each of 4 chosen colors can give left or right sock; \(C^4_{10}\) - total # of ways to choose 4 socks out of 10.

What solution was given in the book for 41/42?

May i knw the logic behind this? m not getting the numerator part ..

If 4 out of 5 pairs of socks will give one sock, we won't have a matching pair, we'll have 4 different color socks and this is exactly what we are counting in the numerator.

Re: There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yell [#permalink]

Show Tags

08 Mar 2014, 05:02

2

This post received KUDOS

I solved this one be listing method

Prob of at least getting a pair = 1 -prob(all different at four attempts) = 1-( 1 x 8/9 x 6/8 x 4/7) = 1-8/21= 13/21

a) 1 st attempt = getting any color =1 b) 2nd attempt = not getting the color picked in a). = 8/9 c) 3rd attempt = not getting the two colors above = 6/8 d) not getting any of the four colors above = 4/7

Why we took 2^4 ? what if we want to solve it by straight forward method ? that is considering P ( getting two socks atleast of same color ) ?

Bunuel wrote:

nonameee wrote:

There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yellow, 2 green. You select randomly four socks together. What is the probability that you'll get at least two of the same color?

"Probability that you'll get at least two of the same color" - means at least one pair (one pair or two pairs out of 4 socks).

P(at least one pair)=1-P(no pair) --> no pair means all socks must be of different colors --> \(P=1-\frac{C^4_5*2^4}{C^4_{10}}=\frac{13}{21}\).

\(C^4_5\) - # of ways to choose 4 different colors out of 5, basically # of ways to choose which 4 color socks will give us one sock (in this case we obviously will have 4 different colors); \(2^4\) - each of 4 chosen colors can give left or right sock; \(C^4_{10}\) - total # of ways to choose 4 socks out of 10.

Why we took 2^4 ? what if we want to solve it by straight forward method ? that is considering P ( getting two socks atleast of same color ) ?

Bunuel wrote:

nonameee wrote:

There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yellow, 2 green. You select randomly four socks together. What is the probability that you'll get at least two of the same color?

"Probability that you'll get at least two of the same color" - means at least one pair (one pair or two pairs out of 4 socks).

P(at least one pair)=1-P(no pair) --> no pair means all socks must be of different colors --> \(P=1-\frac{C^4_5*2^4}{C^4_{10}}=\frac{13}{21}\).

\(C^4_5\) - # of ways to choose 4 different colors out of 5, basically # of ways to choose which 4 color socks will give us one sock (in this case we obviously will have 4 different colors); \(2^4\) - each of 4 chosen colors can give left or right sock; \(C^4_{10}\) - total # of ways to choose 4 socks out of 10.

What solution was given in the book for 41/42?

Can you please tell me which part of below explanation is not clear?

\(C^4_5\) - # of ways to choose 4 different colors out of 5, basically # of ways to choose which 4 color socks will give us one sock (in this case we obviously will have 4 different colors); \(2^4\) - each of 4 chosen colors can give left or right sock.

As for direct approach: it would be lengthier way to get the answer. You should count two cases: A. one par of matching socks with two socks of different color; B. two pairs of matching socks. _________________

There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yell [#permalink]

Show Tags

25 Jul 2014, 03:16

1

This post received KUDOS

Expert's post

kiranpradhan wrote:

Total Number of Possible Combination= 10C4= 210

Total number of Combination where socks is not of same colour= 5C4= 5

Probability of Same= 1- 5/210= 41/42

PS: In socks there is nothing as left & right. So the factor of 2^4 is not required.

Hope it is clear & book is right!

The correct answer is 13/21, not 41/42. The point is that each out of 4 color socks you are selecting can give either first or second sock. Please read the whole discussion above. _________________

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

London is the best kept secret of the corporate world. It is English speaking and time delayed by only 5 hours. That means when London goes home at 5...