Use the following scenario for the next four problems. Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. The sample space is S = {Green1, Green2, Green3, Green4, Green5, Yellow1, Yellow2, Yellow3} G = card drawn is green E = card drawn is even-numbered P(G|E) = Round answer to four decimal places, if necessary. Use the following scenario from Question 5. Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. The sample space is S = {Green1, Green2, Green3, Green4, Green5, Yellow1, Yellow2, Yellow3} G = card drawn is green E = card drawn is even-numbered P(G and E) = Round answer to four decimal places, if necessary. Use the following scenario for the next four problems. Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. The sample space is S = {Green1, Green2, Green3, Green4, Green5, Yellow1, Yellow2, Yellow3} G = card drawn is green E = card drawn is even-numbered P(G or E) = Round answer to four decimal places, if necessary. Use the following scenario for the next four problems. Suppose that you have eight cards. Five are green and three are yellow. The five green cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. The sample space is S = {Green1, Green2, Green3, Green4, Green5, Yellow1, Yellow2, Yellow3} G = card drawn is green E = card drawn is even-numbered Are G and E mutually exclusive? No, P(E or G) = P(E) + P(G) Yes, P(E or G) = P(E) + P(G) Use the following information to answer the next four exercises. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, with replacement. Let G = first card is green Let G2 second card is green Find P(G1 AND G2). Use the following information from Question 9. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, with replacement. Let G = first card is green Let G = second card is green Find P(at least one green). Round answers to four decimal places. Hint: Use the complement rule P(A)+P(A)=1. The complement of "at least one green" is "no green" or "both cards are yellow." Use the following information from Question 9. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, with replacement. Let G = first card is green Let G = second card is green Are G2 and G independent events? Explain why or why not. Yes, since we are sampling with replacement, choosing a green card first has no affect on the probability of choosing a green card second. No, since we are sampling with replacement, choosing a green card first affects the probability of choosing a green card second. Use the following information from Question 9. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, with replacement. Let G = first card is green Let G = second card is green Find P(G2|G1). Round answers to four decimal places, if necessary.