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There are 5 green, 3 yellow and 4 red socks in a drawer. What is the probability of picking out a yellow sock?

What is probability to get 3 balls which are red, blue and yellow?Probability of picking some color combinations of socksFind the probability that at least two of the chosen socks have the same color out of 18 socks- 2 pairs brown,3 pairs blue,4 pairs yellow.Probablity of two randomly selected socks are different color?3 Drawers and 2 kind of socks, what is the probability that you get a pair (red or black)?Probability of getting a pair of socks from a drawer if three are drawnFinding the probability that $2$ socks are the same colorProbability that $1$ red ball, $2$ green balls, and $2$ yellow balls will be selectedProbability of picking matching socks, after partitioning the drawer.Work out the probability that my odd socks are specifically targeted by sock stealing gnomes.

2

1

$begingroup$

My drawer contains 4 blue socks, 5 red socks, and 3 yellow socks. If I randomly pull 2 socks at the same time, what is the probability that the socks are the same color?

I know that the probability that the first sock is blue is $frac514=frac28
$. But I do not know how to calculate the probability that the first two socks are blue.

probability combinatorics

share|cite|improve this question

edited Sep 13 '17 at 15:52

Community♦

1

asked Aug 30 '13 at 1:25

DHShah01DHShah01

149115

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Do you know how to find the probability that the first sock is blue? How about the probability that the first two socks are both blue?
  $endgroup$
  – Adriano
  Aug 30 '13 at 1:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  P(1st sock is blue) = 2/7 P(1st 2 socks being blue) = ??
  $endgroup$
  – DHShah01
  Aug 30 '13 at 1:28
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Can you explain how you got the $2/7$?
  $endgroup$
  – Adriano
  Aug 30 '13 at 1:30
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What have you tried? We will be able to help you more if we know where you are getting stuck.
  $endgroup$
  – dfeuer
  Aug 30 '13 at 1:45
  
  

  
  
  
  

add a comment | 

2

1

$begingroup$

My drawer contains 4 blue socks, 5 red socks, and 3 yellow socks. If I randomly pull 2 socks at the same time, what is the probability that the socks are the same color?

I know that the probability that the first sock is blue is $frac514=frac28
$. But I do not know how to calculate the probability that the first two socks are blue.

probability combinatorics

share|cite|improve this question

edited Sep 13 '17 at 15:52

Community♦

1

asked Aug 30 '13 at 1:25

DHShah01DHShah01

149115

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Do you know how to find the probability that the first sock is blue? How about the probability that the first two socks are both blue?
  $endgroup$
  – Adriano
  Aug 30 '13 at 1:27
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  P(1st sock is blue) = 2/7 P(1st 2 socks being blue) = ??
  $endgroup$
  – DHShah01
  Aug 30 '13 at 1:28
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Can you explain how you got the $2/7$?
  $endgroup$
  – Adriano
  Aug 30 '13 at 1:30
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What have you tried? We will be able to help you more if we know where you are getting stuck.
  $endgroup$
  – dfeuer
  Aug 30 '13 at 1:45
  
  

  
  
  
  

add a comment | 

$begingroup$

My drawer contains 4 blue socks, 5 red socks, and 3 yellow socks. If I randomly pull 2 socks at the same time, what is the probability that the socks are the same color?

I know that the probability that the first sock is blue is $frac514=frac28
$. But I do not know how to calculate the probability that the first two socks are blue.

probability combinatorics

share|cite|improve this question

edited Sep 13 '17 at 15:52

Community♦

1

asked Aug 30 '13 at 1:25

DHShah01DHShah01

149115

$endgroup$

share|cite|improve this question

edited Sep 13 '17 at 15:52

Community♦

1

asked Aug 30 '13 at 1:25

DHShah01DHShah01

149115

share|cite|improve this question

edited Sep 13 '17 at 15:52

Community♦

1

asked Aug 30 '13 at 1:25

DHShah01DHShah01

149115

edited Sep 13 '17 at 15:52

Community♦

1

edited Sep 13 '17 at 15:52

Community♦

1

asked Aug 30 '13 at 1:25

DHShah01DHShah01

149115

asked Aug 30 '13 at 1:25

DHShah01DHShah01

149115

2 Answers
2

active

oldest

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7

$begingroup$

You have $14$ socks, so there are $14 choose 2 = 91$ ways can you pull $2$ socks out from that pile. Of those $91$ ways, you can get pairs by picking two blues, two reds, or two yellows. There are $4 choose 2 = 6$ ways to pick blue socks, $7 choose 2 = 21$ ways to pick red socks, and $3 choose 2 = 3$ ways to pick yellow socks. So there are $30$ possible "good" outcomes out of $91$ total, so the probability is $frac3091 approx 32.967%$

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answered Aug 30 '13 at 1:49

AvrahamAvraham

2,5271131

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add a comment | 

8

$begingroup$

As Adriano pointed, we gonna split this problem in 3 sub-problems. What's the probability of drawing a 2 blue socks in the first 2 drawing. It's:

$$frac414 times frac313 = frac12182$$

Now what's the probability of drawing 2 red socks? It's:

$$frac714 times frac613 = frac42182$$

And the final sub-problem, what's the probability of drawing 2 yellow socks? It's:

$$frac314 times frac213 = frac6182$$

Now we add up this 3 fractions and we end up with:

$$frac12182 + frac42182 + frac6182 = frac60182 approx 32.97 %$$

share|cite|improve this answer

answered Aug 30 '13 at 1:48

Stefan4024Stefan4024

30.6k63579

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add a comment | 

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7

$begingroup$

You have $14$ socks, so there are $14 choose 2 = 91$ ways can you pull $2$ socks out from that pile. Of those $91$ ways, you can get pairs by picking two blues, two reds, or two yellows. There are $4 choose 2 = 6$ ways to pick blue socks, $7 choose 2 = 21$ ways to pick red socks, and $3 choose 2 = 3$ ways to pick yellow socks. So there are $30$ possible "good" outcomes out of $91$ total, so the probability is $frac3091 approx 32.967%$

share|cite|improve this answer

answered Aug 30 '13 at 1:49

AvrahamAvraham

2,5271131

$endgroup$

add a comment | 

7

$begingroup$

You have $14$ socks, so there are $14 choose 2 = 91$ ways can you pull $2$ socks out from that pile. Of those $91$ ways, you can get pairs by picking two blues, two reds, or two yellows. There are $4 choose 2 = 6$ ways to pick blue socks, $7 choose 2 = 21$ ways to pick red socks, and $3 choose 2 = 3$ ways to pick yellow socks. So there are $30$ possible "good" outcomes out of $91$ total, so the probability is $frac3091 approx 32.967%$

share|cite|improve this answer

answered Aug 30 '13 at 1:49

AvrahamAvraham

2,5271131

$endgroup$

add a comment | 

$begingroup$

You have $14$ socks, so there are $14 choose 2 = 91$ ways can you pull $2$ socks out from that pile. Of those $91$ ways, you can get pairs by picking two blues, two reds, or two yellows. There are $4 choose 2 = 6$ ways to pick blue socks, $7 choose 2 = 21$ ways to pick red socks, and $3 choose 2 = 3$ ways to pick yellow socks. So there are $30$ possible "good" outcomes out of $91$ total, so the probability is $frac3091 approx 32.967%$

share|cite|improve this answer

answered Aug 30 '13 at 1:49

AvrahamAvraham

2,5271131

$endgroup$

share|cite|improve this answer

answered Aug 30 '13 at 1:49

AvrahamAvraham

2,5271131

answered Aug 30 '13 at 1:49

AvrahamAvraham

2,5271131

answered Aug 30 '13 at 1:49

AvrahamAvraham

2,5271131

8

$begingroup$

As Adriano pointed, we gonna split this problem in 3 sub-problems. What's the probability of drawing a 2 blue socks in the first 2 drawing. It's:

$$frac414 times frac313 = frac12182$$

Now what's the probability of drawing 2 red socks? It's:

$$frac714 times frac613 = frac42182$$

And the final sub-problem, what's the probability of drawing 2 yellow socks? It's:

$$frac314 times frac213 = frac6182$$

Now we add up this 3 fractions and we end up with:

$$frac12182 + frac42182 + frac6182 = frac60182 approx 32.97 %$$

share|cite|improve this answer

answered Aug 30 '13 at 1:48

Stefan4024Stefan4024

30.6k63579

$endgroup$

add a comment | 

8

$begingroup$

As Adriano pointed, we gonna split this problem in 3 sub-problems. What's the probability of drawing a 2 blue socks in the first 2 drawing. It's:

$$frac414 times frac313 = frac12182$$

Now what's the probability of drawing 2 red socks? It's:

$$frac714 times frac613 = frac42182$$

And the final sub-problem, what's the probability of drawing 2 yellow socks? It's:

$$frac314 times frac213 = frac6182$$

Now we add up this 3 fractions and we end up with:

$$frac12182 + frac42182 + frac6182 = frac60182 approx 32.97 %$$

share|cite|improve this answer

answered Aug 30 '13 at 1:48

Stefan4024Stefan4024

30.6k63579

$endgroup$

add a comment | 

$begingroup$

As Adriano pointed, we gonna split this problem in 3 sub-problems. What's the probability of drawing a 2 blue socks in the first 2 drawing. It's:

$$frac414 times frac313 = frac12182$$

Now what's the probability of drawing 2 red socks? It's:

$$frac714 times frac613 = frac42182$$

And the final sub-problem, what's the probability of drawing 2 yellow socks? It's:

$$frac314 times frac213 = frac6182$$

Now we add up this 3 fractions and we end up with:

$$frac12182 + frac42182 + frac6182 = frac60182 approx 32.97 %$$

share|cite|improve this answer

answered Aug 30 '13 at 1:48

Stefan4024Stefan4024

30.6k63579

$endgroup$

share|cite|improve this answer

answered Aug 30 '13 at 1:48

Stefan4024Stefan4024

30.6k63579

answered Aug 30 '13 at 1:48

Stefan4024Stefan4024

30.6k63579

answered Aug 30 '13 at 1:48

Stefan4024Stefan4024

30.6k63579