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?
(In reply to
solution by Charlie)
The UBASIC program
10 for I=1 to 100
20 T=T+(I//100)^100
30 next
40 print T:print 1//T
gives the probability as
1000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000//1572114066370548760471707147936720868
43814311171382380612596108831201947669658622317126645748904454905428999917816240
71223251083032970727525702989512398590978629099740445007340629219956439236395573
133
(the double / is an artifact of the UBASIC program) There are 200 digits each in the numerator and the denominator.

Posted by Charlie
on 20060518 13:49:42 