Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. G = card drawn is green E = card drawn is even-numbered a. List the sample space. b. P (G) = c. P (G | E) = d. P (G AND E) = e. P (G OR E) = f. Are G and E mutually exclusive? Justify your answer numerically. Exercise 2 Refer to the previous problem. Suppose that this time you randomly draw two cards, one at a time, and with replacement. G1 = first card is green G2 = second card is green a. Draw a tree diagram of the situation. b. P (G1 AND G2) = c. P (at least one green) = d. P (G2 | G1) = e. Are G2 and G1 independent events? Explain why or why not. Exercise 3 Refer to the previous problems. Suppose that this time you randomly draw two cards, one at a time, and without replacement. G1= first card is green G2= second card is green a. Draw a tree diagram of the situation. b. P (G1 AND G2) = c. P(at least one green) = d. P (G2 | G1) =