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?

Using excel to set up a simulation, I get that the expected number of pills left in the bottle is 7.38.  So, 7 or 8.  My skills at this are not stellar, so there is a chance I am wrong.

Posted by Kenny M on 2020-08-19 12:37:17