Bean removal
A pot contains 75 white beans and 150 black ones. Next to the pot is a large pile of black beans.
A somewhat demented cook removes the beans from the pot, one at a time, according to the following strange rule: He removes two beans from the pot at random. If at least one of the beans is black, he places it on the bean-pile and drops the other bean, no matter what color, back in the pot. If both beans are white, on the other hand, he discards both of them and removes one black bean from the pile and drops it in the pot.
At each turn of this procedure, the pot has one less bean in it. Eventually, just one bean is left in the pot. What color is it?
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2 solutions
Moderator note:
- You have to explain why these can be considered as "independent events".
- The solution has to apply to all possible ways of removing beans, instead of just the particular approach that you chose.
We can treat the removal of 1 black bean and the removal of (2 white beans+one black bean) as independent events. First of all remove the black beans. 75 White remain. Now remove whites in twos. 1 White and 37 Black remain. Now remove all blacks. 1 White remains.