There are 12 counters in a box, 5 red and 7 blue. 2 counters are taken out at random without replacement, what is the probability that they are the same colour?

We need to consider two possibilities, you could either pick out two blues or two reds. To find the total probability we work it out for each individually and then add them together. We can find the probability of choosing a particular counter by dividing the number of counters of that colour left in the box, by the total number of counters left in the box.Red- first pick = 5/12 second pick = 4/11One following the other so total probability is 5/12 * 4/11 = 20/132Blue 7/12 * 6/11 = 42/132 Finally add them together to get 62/132 as the result.