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

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

Answer 2

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