Joe has two bottles of seasick pills, each stocked with 40 pills, which he takes with him on his ocean voyage.
During the trip, each time he takes a pill he chooses one of the two bottles at random with equal probability. Eventually one will run out and he's left with the other. When whichever is the first to run out does so, what's the expected value of the number of pills left in the other bottle?
Let's assume that instead of choosing the pills at random, Joe tosses a coin to decide which bottle to choose from.
Then we have binomial(80, 40)/2^80*80 pills for the moment at which one bottle is empty, which is binomial(80, 40)/2^79 or 7.1142303....
This corresponds to the number of pills left in the other bottle, as determined by Jer and Kenny.
Edited on August 19, 2020, 11:40 pm
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Posted by broll
on 2020-08-19 23:14:29 |
An observation
