Question

Show your math to get MEDAL. Probability - If you pull out two socks (then a 3rd) from a sock drawer with two different kinds of socks, what is the chance of getting a complete pair on the 3rd random pick?

Answer 1

probability = number of favorable / number of total

Answer 2

If I stick my hand into my sock drawer, on the 2nd pick I will either have a pair or two different socks; on the 3rd pick, there is a 100% chance I'll make a pair. I'm wondering how to represent that mathematically.

Answer 3

AB
BA
already picked

A || B
3rd either A or B

So end will be either ABA
or BAB
or BAA
or ABB

Answer 4

I guess I could already have a pair--tho unlikely, since I do this every day.
I rarely get a pair on the first try.

Answer 5

lol

Answer 6

this is called pigeon hole principle

Answer 7

if there are only two colors, i would say \(100\%\) for absolute sure you will have a pair on the third pick

Answer 8

you have three pigeons (socks) and 2 pigeon holes (2 colors)

Answer 9

pigeons smidgeons, it is just obvious

Answer 10

a pigeon hole is going to have more than one pigeon :)

Answer 11

ahh, but I want to see the math misty1212

Answer 12

Imagine you have white socks and black socks mixed. You pick 3 socks.
you are guaranteed to pick 2 socks of the same color on the third draw. This is mathematically called the piegon hole principle.

Answer 13

"for natural numbers k and m, if n = km + 1 objects are distributed among m sets, then the pigeonhole principle asserts that one of the sets will contain at least k + 1 objects.[3] For arbitrary n and m this generalizes to k + 1 = ⌊(n - 1)/m⌋ + 1, where ⌊...⌋ is the floor function."
haaaaaa, wikipedia is awesome:

http://en.wikipedia.org/wiki/Pigeonhole_principle#Sock-picking