If I have 3 bags of marbles containing an even number of marbles coloured say, 10 red in the first bag, 6 green in second bag, 4 blue in third. If I then draw marbles at random from any bag to make pairs without replacement so all pairs are enumerated (there will be 10 pairs in this case). What is the probability that I will end up with at least 2 pairs of red marbles?
And similarly how would I find the probability of obtaining at least one pair with one red and one green marble (the ordering is not important).
Ive been using a random sampling method to estimate this, but would be great if anyone could give me a hint as to how to solve this properly.