Problem 1: Suppose a jar has four red marbles and three blue ones. Round to three decimal places) a. Suppose two marbles are selected WITHOUT REPLACEMENT. What is the probability that the first one is blue and the second one is red? (Answer: 3/7*4/6 = 0.286)

b. Suppose two marbles are selected WITH REPLACEMENT. What is the probability that the first one is blue and the second one is red? (Answer: 3/7*4/7 = 0.245)

c. Suppose two marbles are selected WITHOUT REPLACEMENT. What is the probability that all are red? (4/7 *3/6 = 0.286)

Problem 2: Suppose two cards are drawn from a standard deck of 52 cards without replacing the first one before drawing the second one. a. Are the outcomes of the two cards independent? (No)

b. What is the probability of drawing a red card on the first draw and a red card on the second draw? (26/52 * 25/51 = 0.245

c. What is the probability of drawing a king on the first draw and a king on the second draw? (4/52 * 3/51 = 0.005

d. What is the probability of drawing a spade on the first draw and a space on the second draw? (13/52 *12/51 = 0.059

Problem 3: Suppose two cards are drawn from a standard deck of 52 cards and the first one is replaced before drawing the second one. a. Are the outcomes of the two cards independent? (Yes)

b. What is the probability of drawing a red card on the first draw and a red card on the second draw? (26/52 * 26/52 = 0.25)

c. What is the probability of drawing a king on the first draw and a king on the second draw? (4/52 * 4/52 = 0.006)

d. What is the probability of drawing a spade on the first draw and a space on the second draw? (13/52 *13/52 = 0.063)