Chips drawn from a bag

Question

There are 5 blue, 3 yellow and 4 red chips in a bag. You draw two chips out of the bag without replacement. What is the probability of pulling out one blue and one red chip?

Answer 1

Hi Jess,

The probability of getting a blue chip on the first draw is 5/12 since 5 of the 12 chips are blue. Then there are 11 chips left and 4 are red so that probability is 4/11. This combined probability is 5/12 * 4/11 = 5/33.

The other possibility is that a red chip is drawn first, which is 4/12, and then a blue chip is drawn which is 5/11. This combined probability is 4/12 * 5/11 = 5/33.

The total probability of one of these events happening is then 5/33 + 5/33 = 10/33.

Please let me know if I can be more helpful, thanks!

Joe