*ANSWER* Homework 1 Problem 3
I get 1/2 for the following problem. The answer key says 2/3. What am I missing?
P(choosing 1st bag)*P(Second ball is Black/First is Black) = (1/2) * (1*1) = 1/2
P(choosing 2nd bag)*P(Second ball is black/First is black) = (1/2) *(0*(1/2)) = 0
Final probability = Sum of the above = 1/2
3. We have 2 opaque bags, each containing 2 balls. One bag has 2 black balls and the other has a black ball and a white ball. You pick a bag at random and then pick one of the balls in that bag at random. When you look at the ball, it is black. You now pick the second ball from that same bag. What is the probability that this ball is also black?
