Martin has a drawer containing 14 red socks,18 blue scoks and some green socks,all mixed up together.If Martin pulls out one socks,the probability that it will be green is 1/3.
1)How many green socks are in the drawer.
2)If he takes out 3 socks,what is the probaility that he will get a matching pair.
3)If he takes out 2 socks ,what is the probability that he will get a matching pair.
1) let # of green socks be x
p(green sock pulled) = x/(14+18+x) = 1/3
Solving, x= 16
2) p(will get a matching pair out of 3 socks)
= 1 - p(three socks are unique)
= 1 - ((14*16*18)/(48*47*46))
= 1039/1081
3) P (will get a matching pair out of 2 socks)
= p(both red) + p(both blue) + p(both green)
= (14/48)*(13/47) + (18/48)*(17/47) + (16/48)*(15/47)
= 91/262
Akamai, please comment. Thanx