There are 7 white socks and 4 black socks in a drawer. Two socks are taken out at random without replacement. Work out the probability that the two socks are the same colour

The probability of pulling out two socks of the same colour is n/m*(n-1)/(m-1) where n is the initial number of that type of sock and m is the total number of socks in the drawer. The reason that we take 1 away from n and m is because a sock has been taken away from the drawer, and this means the probability of picking that kind of sock again has changed. 

Initially there are 7+4 = 11 socks in the drawer.

The probability of picking 2 white socks is 7/11 * 6/10 = 0.382

The probability of picking 2 black socks is 4/11*3/10 = 0.109

Therefore, to find the probability of picking two of the same colour of sock, we add the probability of picking two white socks and the probability of finding two black socks together. 

0.382 + 0.109 = 0.491