There are two black socks and one gray sock in a drawer. Without looking, Phil selects two socks. Find the sample space of the experiment. What is the probability that Phil selects two black socks?

Question

I would appreciate an answer, thank you! :D

Answer 1

The sample set is, taking the order as significant (B=black, G=gray):

BB BG GB

There are only two results of taking two socks out of the drawer: 2 black socks or one of each colour. There's a probability of 1/3 of selecting the gray sock first and a certainty of selecting a black sock second; there's a probability of 2/3 of selecting a black sock first and a 1/2 probability of selecting another black sock making the combined probability 2/3*1/2=1/3. The probability of selecting two socks of a different colour is also 1/3.