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# MTH 157 Week 2 Checkpoint Solutions

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Date Created: 11/06/15

Show Work When Needed Math 157 Math for Elementary Teachers II 2. If a single letter is drawn from the sem,a,t,h,e,i,c,swhat is the probability that the letter drawn is a member of the set m,a,t,h ? SOLUTION 4 / 8 = 0.5 In Exercises 3–8, consider the experiment of rolling a single die. 6. What is the probability of rolling a number that is divisible by 2 or 3? SOLUTION Numbers divisible by 2 or 3: {2, 3, 4, 6} P{divisible by 2 or 3}: 4 /6 = 2/3 In Exercises 9–16, consider the experiment of selecting a card from an ordinary deck of 52 playing cards and determine the probability of the stated event. 12. A card that is not a king and not a spade is drawn. SOLUTION (52 – 4 – 12) / 52 = 36 / 52 = 9 / 13 In Exercises 17–20, consider a bowl containing 36 different slips of paper. Ten of the slips of paper each contain one of the set of digits 0 through 9 and 26 slips each contain one of the 26 letters of the alphabet. Determine the probabilities of the events specified. 18. Drawing one slip, what is P (slip contains a vowel)? SOLUTION P(slip contains a vowel) = 5 / 36 In Exercises 24–27, consider the experiments involving rolling a single die once. Give the probabilities of the event described. 28. Suppose that an experiment has five separate mutually exclusive outcomes: A, B, C, D, and E. If the sample space for the experiment is a uniform sample space, what is P(A or B)? SOLUTION P(A or B) = P(A) + P(B) – P(AB) = 0.2 + 0.2 + 0.0 = 0.4 32. In a family with two children, what are the probabilities of the following outcomes, assuming that the birth of boys and girls is equally likely? a. Both are boys. b. The first is a girl and the second a boy. c. Neither is a girl. d. At least one is a girl. SOLUTION a) P(2 boys) = 0.5 * 0.5 = 0.25 b) P(first girt, second boy) = 0.5 * 0.5 = 0.25 c) P(neither is a girl) = P(2 boys) = 0.5 * 0.5 = 0.25 d) P(at least one girl) = 1 – P(2 boys) = 0.75 Section 9.1 pp. 505507 #36 2 1 If P(A) = and P(B) = and P(A and B) = 0, what can you say about P(A or B)? 3 6 SOLUTION P(A or B) = P(A) + P(B) – P(A and B) = 2/3 + 1/6 – 0 = 5/6 Section 9.2 pp. 515517 #4 4. How many three-symbol codes (letter-number-number) can be made from the letters S, P, Y, and two digits from the set {0,1,2,3,4,5,6,7,8,9} without repetition? SOLUTION 3 * 10 * 9 = 270 different codes Section 9.2 pp. 515517 #10 10. Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What is the probability that both are spades if the first card drawn was a spade? SOLUTION 12/51 = 4/17 Section 9.2 pp. 515517 #16 16. A pair of dice are rolled and the sum on their upturned faces is recorded. What is the probability that the sum showing is 8, given that one die is showing a 5? SOLUTION Possible sums with 2 dice given that one of them shows a 5: 6 + 5 = 11 Ways to get a sum of 8 given that one die is showing a 5: 2 (3, 5) and (5, 3). P(sum is 8 given that one die is a 5) = 2 / 11 Section 9.2 pp. 515517 #20 20. A box contains two black balls and three gold balls. Two balls are randomly drawn in succession from the box. a. If there is no replacement, what is the probability that both balls are black? b. If there is replacement before the second draw, what is the probability that both balls are black? SOLUTION a) P(2 black) = (2/5) * (1/4) = 1/10 b) P(2 black, with replacement) = (2/5)*(2/5) = 4/25 Section 9.2 pp. 515517 #22 22. In the tests of a new pharmaceutical product, data were collected for use in the approval process required by the U.S. Food and Drug Administration (FDA). Some participants were given a placebo, an inert substance that looks like the drug; others were given the drug. The data are shown in the following table: No Help Help Drug 22 47 Placebo 31 20 What is the probability that: A. the participants perceived that their “medication” helped if they received the drug? B. the participants perceived that their “medication” helped if they received the placebo? C. the participants perceived that their “medication” helped? SOLUTION a) 47 / (22 + 47) = 47 / 69 b) 20 / (31 + 20) = 20 / 51 c) (47 + 20) / (22 + 47 + 31 + 20) = 67 / 120 Section 9.2 pp. 515517 #26 26. Jack is taking a four-item true–false test. He has no knowledge about the subject of the test and decides to flip a coin to answer the items. A. What is the probability that he receives a perfect score? B. What is the probability on a 10-item test? SOLUTION a) (1/2)^4 = 1/16 b) (1/2)^10 = 1/1024

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