## mathishard2 Group Title 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? one year ago one year ago

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1. izzy56658989 Group Title

1/2 chances or 5/10

2. mathishard2 Group Title

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

3. izzy56658989 Group Title

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

4. mathishard2 Group Title

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 Group Title

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 Group Title

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

7. izzy56658989 Group Title

there's ur denominator

8. satellite73 Group Title

he picks one sock it is some color

9. satellite73 Group Title

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

10. izzy56658989 Group Title

exactly it never said they were the same colors

11. satellite73 Group Title

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

12. satellite73 Group Title

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

13. satellite73 Group Title

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 Group Title

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