Two boxes contain 6 balls each. Each ball is either red, blue or green and has a number written on it. In the ?rst box all of the balls are blue, two are marked 0 and four are marked 1. In the second box there are four green balls - two marked 0 and two are marked 2 - and two red balls one marked 0 and one marked 2. The boxes can be pictured as follows:

B0 B0 B1 B1 B1 B1 Box one / G0 G0 G2 G2 R0 R2 Box two

Each ball in the boxes has both a color and a number on it. The key for the color is as follows: R = Red, B = Blue, G = Green. Answer the following questions below based on the contents of the boxes.

(a) One ball is drawn at random from Box 1. What is the probability that the ball drawn has a number 1 on it?

(b) One ball is drawn at random from Box 2. What is the conditional probability that the ball drawn is green given that it has the number 2 on it?

(c) Two balls are drawn at random with replacement from Box 2. What is the probability that at least one of the balls drawn has the number 0 on it?

(d) Two balls are drawn at random without replacement from Box 2. What is the probability that at least one of the balls drawn has the number 0 on it?

(e) A person chooses a box at random (either Box 1 or Box 2) and draws two balls without replacement from that box. What is the conditional probability that both of the balls are blue given that the sum of the numbers on the balls is odd?