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Probability of Matching Socks

by Clarence
(Deatsville, AL, USA)










































you have 4 red socks and 2 blue socks. What is the probability of a match after picking 2 socks?

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Mar 11, 2012
Probability of Matching Socks
by: Staff


Question:

by Clarence
(Deatsville, AL, USA)

you have 4 red socks and 2 blue socks. What is the probability of a match after picking 2 socks?


Answer:

There is a formula which you can use to calculate possible combinations of picking two socks at a time:

C(n,r) = n! / r! (n - r)!

0 ≤ r ≤ n.
n = number of elements in the set { r1, r2, r3, r4, b1, b2 } = 6
r = number of elements selected = 2

Order is not important

Repetition is not allowed



Selecting any 2 elements from the 6 possible choices
n = number of elements = 6
r = number of elements selected = 2

C(n,r) = n! / r! (n - r)!


C(5,2) = 6! / 2! (6 - 2)!
C(5,2) = (6*5*4*3*2*1) / 2*1*4*3*2*1
C(5,2) = 6*5 / 2*1
C(5,2) = 30 / 2

C(4,2) = 15

So, if you choose 2 socks at a time, 15 different combinations are possible. These combinations are:

{r1,r2} {r1,r3} {r1,r4} {r1,b1} {r1,b2} {r2,r3} {r2,r4} {r2,b1} {r2,b2} {r3,r4} {r3,b1} {r3,b2} {r4,b1} {r4,b2} {b1,b2}

As you can see, there are 7 combinations of matching socks out of 15 possible combinations.

The chance of getting a matching pair of socks is 7 out of 15

>>> the final answer to your question is: 7/15


Thanks for writing.

Staff
www.solving-math-problems.com



Mar 03, 2014
Teacher
by: Ms.J

This is too complicated. The students get confused. If you simply break it down and separate it, they can get it.
1st-Probability of red is 4/6 x 3/5=12/30….Then Probability of blue is 2/6 x 1/5=2/30. Now add the 2 probabilities 12/30 + 2/30=14/30 and simplify. 7/14. This they can understand.

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