From bag A containing 4 black and 8 blue marbles, 6 marbles are transferred into an empty bag B. Three marbles are now drawn from bag B, and each of them happens to be black.

Determine the probability that a fourth marble drawn from bag B will be black, given that:

(I) The first three marbles are returned to bag B.

(II) None of the first three marbles is returned to bag B.

(In reply to solution by Charlie)

Charlie. I've been trying to match your solution to this problem with a Monte Carlo approach, but with limited success.
Forgive me if I'm wrong, but the second part of your formula for the 'overall a priori probability..' seems to relate to 4 balls being drawn rather than 3.

Posted by Harry on 2010-02-16 15:38:55