A box contains 12 marbles of three different colors – Green, Yellow and Blue – 4 of each.

If you were to close your eyes and pick them at random, how many marbles must you take out to be sure that there are at least two of one color among the marbles picked out ?

The answer is four.

If you were trying to get two marbles of the same colour, and there are three colours, the most you can pick out without two of a colour is three - one of each colour.

Therefore the next one you pick out has to be the same colour as one of the others, so the answer is four.

This problem was a little easy, so I decided to work out the probabilities.

When you pick out the first one, it means there are only three of that colour left. So the probability that the second will be the same is 3/11.

If you didn't get the same colour, then you'll have two different colours, each with three of the same in the bag, and the remaining colour will have four in the bag. This means that the probability of getting a colour you already got is 3/5.

And if you still didn't get a duplicate colour, the next one has a probability of 1, seeing as there is no other different colours.

Posted by Lewis on 2003-06-08 10:24:10