probability of obtaining......

[scatteam_2]

there are four red socks and two blue socks in a drawer. two socks are removed at random. what is the probability of obtaining:

a) 2 red socks?
b) 2 blue socks?
c) one of each colour?


is there some sort of formula u must use to work this out? im stuck
please help and explain step by step
much appreciated =] =]

[the.watchman]

Try taking each sock individually and thinking about the associated probability:

(a)

So the first fraction is basically, when taking out the first sock, there are four red socks out of six
The second fraction is for the second removal, where a red sock had already been removed, so there are three red socks out of five now.

[Duck]

First time you pull out a sock there's a 4/6 chance of it being red because there are 4 red socks out of 6 total socks. The second time you pull out a sock there's only 3 red socks out of a total of 5 socks so the probability of getting a red sock is 3/5. Hence you multiply 4/6 by 3/5 to get 12/30 which equals 2/5. Do the same with blue socks (2/6 * 1/5) and then for one of each you add the probabilities of getting blue first then red and red first then blue (2/6 * 4/5 + 4/6 * 2/5)