A bag contains 12 red balls and 8 yellow balls. Three balls are taken out of the bag and on each occasion, the ball is not returned to the bag. Find the probability of obtaining two red balls and a yellow ball in any order? - Answers

In essence there are only 3 possibilities: RRY RYR YRR The sum of the odds of these three things is the possibility of one of them happening. The order does matter in this, because which one you draw first affects the odds of which one you draw second in this scenario. There's 20 balls to begin with, and each time we remove a ball we're decreasing the total number, so the odds break down like this: RRY: 12/20 * 11/19 * 8/18 RYR: 12/20 * 8/19 * 11/18 YRR: 8/20 * 12/19 * 11/18 Because of the specific circumstances the odds of each are actually the same (because we're decreasing the total pool and the individual pools at the same rate in all three, essentially they're the same numbers in different orders). Each has a roughly 15.2% chance, and adding those odds together gives us the odds of one of them happening (but it doesn't matter which one). Totaling to a roughly 46.2% chance of drawing some combination of the three. For comparison, there's a 19.2% chance that they come up as RRR, and a mere 4.9% chance that they come up YYY. The odds of two yellows and a red, meanwhile is about 29.4. Note that, because of my rounding this only totals out to 99.7%, but you get the picture. If you need the odds to a more specific decimal point, you can plug in the numbers and get the full totals.