You choose one of two identical looking bags at random. One bag has three black marbles and one white marble. The other has three white marbles and one black marble.
After choosing a bag you draw one marble out at random. You notice it is black. You then put it back and draw another marble out of the same bag at random.
What is the probability that the second marble drawn is black?
(In reply to
no expert by nellie)
The fact that you got a black ball increases the likelihood that it was a blackmajority bag.
Suppose there were a thousand black balls and 1 white ball in one bag and a thousand white balls plus 1 black in the other. In this instance the inference would be even stronger that initially drawing out a black ball makes it more likely that the next will be black also.
The case with only 4 balls in each bag is similar but to a less pronounced extent.

Posted by Charlie
on 20031014 10:42:40 