PRINTABLE VERSION Quiz 12 Question 1 Let A and B be events in a sample space S such that P(A) = 0.38, P(B) = 0.42 and P(A B) = 0.20. Find P(A | B). a) 0.5263 b) 0.2500 c) 0.0238 d) 0.4762 e) 0.9048 f) None of the above. Question 2 Let A and B be events in a sample space S such that P(A) = 23100 , P(B) = 47100 , and P(A B) = 320 . Find P(B | Ac ). Hint: Draw a Venn Diagram to find P(Ac B). a) 0.4156 b) 0.6104 c) 0.1948 d) 2.0435 e) 0.6809 f) None of the above. Question 3 Suppose that A and B are independent events. If P(A) = 910 and P(B) = 25 , find P(A B). a) 0.36 b) 0.13 c) 0.09 d) 0.04 e) 1.00 f) None of the above. Question 4 Quality Control: A company has four photocopy machines A, B, C and D. The probability that a given machine will break down on a particular day is P(A) = 950 P(B) = 15 P(C) = 19100 P(D) = 11100 Assuming independence, what is the probability on a particular day that all machines will break down? a) 0.00132908 b) 0.00000360 c) 0.01000000 d) 0.13290803 e) 0.00075240 f) None of the above. Question 5 A pair of fair dice is cast. What is the probabiliy that at least one of the numbers falling uppermost is a 1, given that the sum of the numbers falling uppermost is even? a) 0.3667 b) 0.4545 c) 0.3056 d) 0.2778 e) 0.1389 f) None of the above. Question 6 Two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the first card drawn is a Spade and the second card drawn is not a Spade? a) 0.1912 b) 0.0588 c) 0.7500 d) 0.1875 e) 0.0577 f) None of the above. Question 7 Suppose we have two urns, Urn 1 and Urn 2. Urn 1 contains 7 red marbles and 9 white marbles. Urn 2 contains 5 red marbles and 13 white marbles. The experiment consists of first choosing an urn with equally likely probability, and then drawing a marble from that urn. What is the probability of choosing Urn 2 and a red marble? a) 0.2813 b) 0.4375 c) 0.7222 d) 0.1389 e) 0.2188 f) None of the above. Question 8 A recording company obtains the blank CDs used to produce its labels from three compact disk manufacturers: I, II, and III. The quality control department of the company has determined that 1% of the compact disks produced by manufacturer I are defective, 7% of those produced by manufacturer II are defective, and 3% of those produced by manufacturer III are defective. Manufacturers I, II, and III supply 36%, 20%, and 44%, respectively, of the compact disks used by the company. What is the probability that a randomly selected label produced by the company will contain a defective compact disk? a) 0.0308 b) 0.0140 c) 0.1100 d) 0.0036 e) 0.0132 f) None of the above. Question 9 Suppose that 9 green balls and 13 purple balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn? a) 0.8182 b) 0.5909 c) 0.6364 d) 0.4091 e) 0.1302 f) None of the above