1. A bag contains 3 balls: 1 blue, 1 red, and 1 green. Suppose I draw 2 balls from the bag with replacement(that is, after drawing the first ball and observing its color, I return it to the bag). Let B be the event of drawing a blue ball in a given draw, R be the event of drawing a red ball and G be the event of drawing a green ball.

a. List all possible outcomes. (2 marks)

b. List all possible outcomes for each of the following events and find the corresponding probabilities. (8 marks)

1. A = {Exactly 1 green ball is drawn}
2. B = {The first ball is red}
3. C = {At least one ball is blue}
4. D = {Both balls are the same color}

c. List all possible outcomes and find the probabilities of the following events. (10 marks: 2 for each)

1. Not C
2. A & C
3. A&D
4. B&D
5. C or D. d.Identify all possible pairs of events defined in part (b) that are mutually exclusive. (3 marks)

e. Verify mathematically that B and D are independent events, while C and D are not. (3 marks)