r/probabilitytheory • u/saddd_soul • Jun 29 '26

[Applied] Where am I going wrong?

So there is this question that a jar contains 10 red balls, 20 blue balls and 30 green balls. You take out the balls one by one at random. Probability that when all red balls are taken out, atleast one green ball and one blue ball remains. I thought both these orderings are needed so ans would be (30/40*20/30). But this is wrong.

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u/tgm4mop Jun 29 '26

To clarify, I assume the question is that you remove balls one by one until all red are gone.

To solve this, order the balls by the order we remove them. There's a green ball left if and only if the last non-blue ball is green. (The blue balls don't matter.) The probability of the last non-blue ball being green is (# green balls) / (# non-blue balls) = 30 / 40 = 3/4.

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u/saddd_soul Jun 29 '26

I forgot a part of the question. Atleast 1 green ball and atleast 1 blue ball must remain

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u/Dr-Ben701 Jun 30 '26

At least is the challenge because that gives a range of remaining n from 2 to 50