Which of the following is not a sample space for the experiment of flipping a coin 3 times? O A. { the last two coin flips are the same, the last two coin flips are different} O B. { the first two coin flips are the same, the first two coin flips are different} O c. {all the flips are heads, there are an odd number of tails} O D. {all the flips are heads, exactly two tails are flipped, there are an odd number of tails} O E. {all the flips are heads, there is at least one tail}Suppose C and A are events in the same sample space for some experiment. Suppose C occurs 45% ofthe time, A happens three out of ten times the experiment is run, and both events occur with probability 0.16. Determine Pr[C U A]. A. 0.14 B. 0.59 C. 0.29 D. 0.75 E. 0.43 Suppose we have a sample space S = {k, l, m, 11}. If it is known that outcome m is twice as likely as outcome )1, Pr[l] = Pr[m], and outcome k occurs one fifth of the time. Determine Pr[n]. 2 A. O A. 15 Suppose B and H are events in the same sample space for some experiment. If we know Pr[B] = 2, Pr[H] = 2, and Pr[B n H] = -, determine Pr[B | H]. 16 O B. W / H O C . 8 15 OD. 24 O E.Suppose D and E are independent events in the same sample space. If we know that Pr [D] = g and Pr [E] = %, determine Pr [D6 n E] A. 9 Lars has 6 different poetry textbooks, 8 different math books and 4 different biology books. He arranges these eighteen books randomly on a shelf. What is the probability that books of the same subject are all together? 6!8!4! A. 18! 1 B_ _ 6 1 C_ 6l8l4! 3!6!8!4! D. 18! 3! 6!8!4! E. A hand of 13 cards is dealt at random from a standard well-shuffled deck of 52 cards. What is the probability that the hand contains exactly 2 spades, given that there are exactly 7 red cards? A.++('3> (3:)(363) <_3: c373 al e a fair six-sided die is being rolled twice. which of the following samples spaces equiprobable second roll less than greater equal to or one both rolls are no even odd only rst a. an sample space b. and s3 c. sg d. s1 s e. none them>