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There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yell

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There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yell [#permalink] New post 27 May 2010, 02:41
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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?

I think it's
[Reveal] Spoiler:
13/21


The book says it's
[Reveal] Spoiler:
41/42
which is in my opinion a mistake.
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Re: Probability question: 10 socks [#permalink] New post 27 May 2010, 03:59
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Expert's post
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?

I think it's
[Reveal] Spoiler:
13/21


The book says it's
[Reveal] Spoiler:
41/42
which is in my opinion a mistake.


I think you are right.

"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?
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Re: Probability question: 10 socks [#permalink] New post 27 May 2010, 04:02
Quote:
What solution was given in the book for 41/42?


I think they've forgotten to multiply by 2^4. But the solution was the same you gave.
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Re: Probability question: 10 socks [#permalink] New post 28 May 2010, 20:26
Thanks for the explanation.


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?

I think it's
[Reveal] Spoiler:
13/21


The book says it's
[Reveal] Spoiler:
41/42
which is in my opinion a mistake.


I think you are right.

"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?
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Re: Probability question: 10 socks [#permalink] New post 28 May 2010, 21:07
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?

I think it's
[Reveal] Spoiler:
13/21


The book says it's
[Reveal] Spoiler:
41/42
which is in my opinion a mistake.


I think you are right.

"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 ?
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Re: Probability question: 10 socks [#permalink] New post 29 May 2010, 02:31
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Re: Probability question: 10 socks [#permalink] New post 06 Mar 2014, 10:37
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?

I think it's
[Reveal] Spoiler:
13/21


The book says it's
[Reveal] Spoiler:
41/42
which is in my opinion a mistake.


I think you are right.

"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 ..
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Re: Probability question: 10 socks [#permalink] New post 07 Mar 2014, 00:21
Expert's post
sanjoo wrote:
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?

I think it's
[Reveal] Spoiler:
13/21


The book says it's
[Reveal] Spoiler:
41/42
which is in my opinion a mistake.


I think you are right.

"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.

Hope it's clear.
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Re: There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yell [#permalink] New post 08 Mar 2014, 04:02
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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
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Re: Probability question: 10 socks [#permalink] New post 12 Mar 2014, 10:52
Dear Bunuel

I did 10c1X1c1 X 8c1X6c1/ 10c4 + 10c1X1c1 X 8c1X1c1/10c4.
Answer is wrong. Please help!

Thanks & regards
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Re: Probability question: 10 socks [#permalink] New post 03 May 2014, 01:00
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?

I think it's
[Reveal] Spoiler:
13/21


The book says it's
[Reveal] Spoiler:
41/42
which is in my opinion a mistake.


I think you are right.

"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?
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Re: Probability question: 10 socks [#permalink] New post 03 May 2014, 03:37
Expert's post
sunny3011 wrote:
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?

I think it's
[Reveal] Spoiler:
13/21


The book says it's
[Reveal] Spoiler:
41/42
which is in my opinion a mistake.


I think you are right.

"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.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yell [#permalink] New post 24 Jul 2014, 17:07
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!
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There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yell [#permalink] New post 25 Jul 2014, 02:16
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.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yell   [#permalink] 25 Jul 2014, 02:16
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