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?

Question

anonymous · Answer

1/2 chances or 5/10

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

there's ur denominator

anonymous · Answer

he picks one sock
it is some color

anonymous · Answer

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

anonymous · Answer

exactly it never said they were the same colors

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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 
$$\frac{5}{45}=\frac{1}{9}$$

anonymous · Answer

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