We have two boxes, each containing three balls: one black and two white in box 1; two black and one white in box 2. we choose one of the boxes at random, where the probability of choosing box 1 is equal to some given p, and then draw a ball.

1. describe the map rule for deciding the identity of the box based on whether the drawn ball is black or white.

2. assuming that p = 1 2 , find the probability of an incorrect decision and compare it with the probability of error if no ball had been drawn.