Quote:
Originally Posted by Rotimi
I could not use Bayes' theorem to solve Problem 1.1 but I thought of an 'alternative' method which gave me the answer 2/3. I want to know if this method is right or not. It's as follows:
Since there are 2 black balls and 1 white ball left are choosing the first black ball, the chances that the second ball is black is 2/3 since there are 3 balls left.
Is this method right or not?

This would have been right if the question had specified that we picked the second ball from all remaining balls. However, the second ball is picked only from the same bag that produced the first (black) ball, so the logic of the problem is different.
For instance, if we changed the statement of the problem to having two bags one with two black balls and one with two white balls, and you picked a bag that produced a black ball, the second ball will be black with probability 100%, notwithstanding that the total remaining balls in both bags are two white and one black.