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.


  1. Anonymous10:02 PM

    Normal distribution? π

  2. Anonymous10:11 PM

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

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

  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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