Hard Jelly Bean Problem

This is somewhat similar to one I posted here years ago, but, I suspect, is much harder. Be warned.

A hat (upside down, of course) contains a black jelly beans and b orange jelly beans. You reach in and randomly remove a jelly bean. If it is black, you return it to the hat with a probability of p, otherwise you eat it. If it is orange, you return it to the hat with a probability of q, otherwise you eat it. What is the probability that the last jelly bean in the hat will be black?/orange?

Note that p and q are independent of each other, and cannot be one.

Good luck.

4 comments:

  1. Normal distribution? π

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  2. This is a trick question on the Cauchy Distribution, isn't it?

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  3. 0, because this person loves black jelly beans and purposefully searches for it to eat it.

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  4. No, dear ones, there is a specific f(a,b,p,q). No trick, just hard. Hey, lookit me--I love hard problems and have touched this one.

    And JFC: I did say "randomly".

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