Ken's POTW
Balls and Urns
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An urn contains two balls, each black or white with even odds.
You pick a ball from the urn. It is black. You replace the ball.
You pick another ball from the urn. What are the odds that
it is also black?
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Do the odds change if prior to picking the first ball in problem 1,
you are told that one of the balls is black, then again your first
pick is black?
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There are two empty urns in a room. You have 50 white balls
and 50 black balls. After you place the balls in the urns,
a random ball will be picked from a random urn.
Distribute the balls (all of them) into the urns to maximize
the chance of picking a white ball.
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You have one white ball and one black ball to place in an urn. What
picking method would you propose to create a probability of 1/3?
That is, if I am picking between A and B based on the outcome of your
method, I will pick A an average of 1 time out of 3. Multiple picks
are allowed (and probably necessary.) This is similar to asking how
to simulate a probability of 1/3 with only a fair coin.
Source: Internet newsgroup rec.puzzles, used as Ken's Puzzle of the Day
3/22&29/94
Solution
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