There are 7 white socks and 4 black socks. 2 are taken at random without replacement. What is the probablity that 2 socks of the same colour are taken?

With a more wordy question like this, it is always best to break it up and write down all of the key pieces of information. So we want to work out the probability of picking: white AND white, OR, black AND black. In probability, AND means 'multiply' and OR means 'add'. So: [P(white) X P(white)] + [P(black) X P(black)] Another importnant part of the question is 'WITHOUT REPLACEMENT'. This means that the probablities will CHANGE when you remove a sock. So: P(first white)= 7/(7+4) P(second white)= 6/(6+4) P(first black)= 4/(7+4) P(second black)= 3/(7+3) P(White and White)= (7/11)X(6/10) = 42/110 P(Black and Black)= (4/11)X(3/10) = 12/110 now we need to add the 2 probablities together: 42/110 + 12/110 = 54/110 = 0.49