Question

A drawer contains n = 5 different and distinguishable pairs of socks (a total of ten socks).
If a person (perhaps in the dark) randomly selects four socks, what is the probability that
there is no matching pair in the sample

total combinations 10C4= 210

Of the 5 matching pairs we have 28 * 5 ways that we can match only one pair when four are selected
(blue, blue, x,y) 8C2= 28
(red,red,x,y) .
.
.
so we get 5*28 combinations where socks match so combinations with no match 210 - 140= 70

probabiliy no match = 70/210

is this righ??

Answer 1

one third?

Answer 2

i get a different answer, but i could be wrong

Answer 3

pick a sock
it is some color
pick another sock
the probability it is different color is \(\frac{8}{9}\)
the probability that the next is different from the first two is \(\frac{6}{8}\) and the probability that the fourth is different from the first three is \(\frac{4}{7}\)

Answer 4

take the product for your answer, it is not one third i don't think

Answer 5

I agree with satellite73, with (8*6*4)/(9*8*7) as anwer.

Answer 6

for sure there are 140 , where socks match right? so now we would have to think if there is anything else missing I guess

Answer 7

it does make sense

Answer 8

you forgot the cases: (blue, blue, red, red) , ...

Answer 9

couldn't they be in the (blue,blue,x,y) x and y could be anything including other matching socks no?

Answer 10

you wrote 8C2. this does ..
oops you're right.

Answer 11

but there's a problem linked to this.
(blue, blue, x,y) with (x,y)=(red,red) means that you count (blue, blue, red,red) here once, but you will count it again when you look at (red, red, x,y) and (x,y)=(blue,blue). Therefore, you count too many stuff in the matching probability, therefore the probability of "no match" is too small.

Answer 12

@arykk

Answer 13

true you are right once again. so there fore we would have to take away those . in that case
210 - 140-10 = 60 combinations where socks don't match.

so the probability would be 60/210 =2/7 = .2857 this would make sense

how come it isn't the same as satellite73 approach? (8*6*4)/(9*8*7) = .3809

Answer 14

@satellite73 @reemii

Answer 15

it's rather 210-140 + something

Answer 16

because it's 210 - (140 - something)
(140 was too big)

Answer 17

this approach is too confusing for me

Answer 18

number of (x,x,y,y) is 5C2 = 10. as you said.
it's ok: (210-140+10)/210 = satellite's answer = 0.38095... !

Answer 19

@arykk I think you can assume you solved the problem your way too.

Answer 20

@reemii thanks!!