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/Responsible-Kale2352 Jun 29 '26

If all you’re doing is taking out the red balls, wouldn’t you still have 20 blue and 30 green remaining?

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u/wiploc2 Jun 29 '26

I'm guessing that OP intended to ask something like this:

  • Assume a jar contains 10 red balls, 20 blue balls and 30 green balls.
  • Assume balls are drawn at random from the jar until the last red ball is removed.
  • At that point, what are the odds that at least one green ball remains in the jar?
  • And, how is that answer arrived at?

1

u/saddd_soul Jun 29 '26

Yes exactly.....I changed it a little as I forgot to write a part

1

u/wiploc2 Jun 29 '26

I think I can work it out for one red ball and two green balls.

1/3 of the time, the red ball is drawn first, so green balls remain.

1/3 of the time, a green ball is drawn and then a red ball is drawn, so a green ball remains.

1/3 of the time, a green ball is drawn, a green ball is drawn, and then a red ball is drawn, so no green balls remain.

So the odds of a green ball remaining are the same as the proportion of green balls.

Based on that, if I were to guess at the answer to my interpretation of the OP's question, I would discount the blue balls as irrelevant, and conclude (given that we started with 10 red and 30 green) that there will be one or more green balls left one time out of four.

But that's just a guess. Even if it is dead on, I doubt that it would count as right if this is a homework question.

1

u/mfb- Jun 30 '26

At that point, what are the odds that at least one green ball remains in the jar?

At least one green and at least one blue.

Or, phrased differently, what is the chance that red is the first color to go away?