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 Marbles in a Jar (Posted on 2006-05-18)
You have a jar that is filled with a hundred marbles, each of them either black or white, but you have no idea how many of each color there are. However, you have been told that all possible quantities of white marbles (from 0 to 100, both inclusive) are equally probable.

You randomly select 100 marbles from the jar one at a time, with replacement, and they are all white. What is the probability that the jar contains only white marbles?

 See The Solution Submitted by tomarken Rating: 3.4000 (5 votes)

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 re: solution -- the exact answer | Comment 6 of 10 |
(In reply to solution by Charlie)

The UBASIC program

`10   for I=1 to 10020    T=T+(I//100)^10030   next40   print T:print 1//T`

gives the probability as

` 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000//15721140663705487604717071479367208684381431117138238061259610883120194766965862231712664574890445490542899991781624071223251083032970727525702989512398590978629099740445007340629219956439236395573133`

(the double / is an artifact of the UBASIC program) There are 200 digits each in the numerator and the denominator.

 Posted by Charlie on 2006-05-18 13:49:42

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