Question

A drawer contains 6 white socks and 10 black socks. If 2 socks are chosen at random, what is the probability that they will have the same color? Please explain!!! I have the SHSAT Exam tomorrow and I need to know how to do this. Thanks.

Answer 1

`|\Omega|=C(16,2)=(16!)/(2!14!)=(15\cdot16)/(2)=120\\|A|=C(6,2)+C(10,2)=(6!)/(2!4!)+(10!)/(2!8!)=(5\cdot6)/(2)+(9\cdot10)/(2)=15+45=60\\\\P(A)=(60)/(120)=(1)/(2)=50\%`

Answer 2

there are 16 socks in the drawer

probablility of 2 white socks or 2 black socks

6/16 *5/15 + 10/16*9/15 no replacement on socks

30/240 + 90/240

120/240

1/2