mathishard2 2 years ago A man has five pairs of socks (no two pairs are the same color). If he randomly selects two socks from a drawer, what is the probability that he gets a matching pair?

• This Question is Open
1. izzy56658989

1/2 chances or 5/10

2. mathishard2

The answer in the book says 1/9...

3. izzy56658989

i never said it was gonna be right there was a half chance i was wrong

4. mathishard2

I'm not trying to show that you're wrong... I just wanted to see if someone could explain this question to me. Because math is hard. And I have a test on probablility tomorrow.

5. izzy56658989

k there's 5 there it's an uneven number which means if u tryed to pair them all up 1 would be left behind

6. izzy56658989

lik if u got rid of that 1 sock and did 4x2 =8+1=9

7. izzy56658989

there's ur denominator

8. satellite73

he picks one sock it is some color

9. satellite73

then there are 9 socks left in the drawer, and only one has the same color as the sock he picked originally

10. izzy56658989

exactly it never said they were the same colors

11. satellite73

so the probability that the next sock he picks has the same color is $$\frac{1}{9}$$

12. satellite73

it is easier to think about it if you imagine picking one at a time instead of two at once

13. satellite73

we can also solve with thinking of picking two at once the number of ways he can pick the two socks out of the total of ten socks is $\dbinom{10}{2}=\frac{10\times 9}{2}=5\times 9=45$ of those 45 ways, 5 of them are pairs that match, so you get the probability as $\frac{5}{45}=\frac{1}{9}$

14. satellite73

i think the first way is easier to envision, but it is a matter of taste i suppose