an urn contains 2 red, 2 white and 1 yellow balls. Three balls are drawn from the urn at random, one at a time. Find the probablility that none of the three are red assuming without replacement

For each step, think through (a) how many balls are in the urn, and (b) how many of those balls satisfy the condition that it is not red. Then divide (b) by (a) to get the probability that for that step you will pull a ball that is not red. Do this for when there are 5 balls in the urn, then 4, then 3, assuming for each step you still have the original 2 red balls still in the urn. Finally, multiply all three probabilities together.

Here's an example of a slightly different problem to show how this works. Suppose there were 10 balls in the urn, and 5 are red, and you ar going to pull 3 without replacement. What is the proability that no red balls are pulled in those 3 draws? For the first draw, the probability of not pulling a red is5/10. Assuming that you don't get a red on that first draw, that still leaves 5 reds and 4 non-reds out of the 9 remaining. So the probability of pulling a non-red on the second draw is 4/10 . And for the third draw it's 3/10. So the probability of not pulling red on all three draws is: (5/10)*(4/9)*(3/8).

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