Nicole Becker - Assignment 1 Complete the following textbook exercises: 2, 8,12, 20, 28, 36, 48, 74, 84 and 88 2. A quality control inspector selects a part to be tested. The part is then declared acceptable, repairable, or scrapped. Then another part is tested. List the possible outcomes of this experiment regarding two parts. There can be at most 9 possible outcomes: (acceptable,acceptable),(acceptable,repairable),(acceptable,scrapped),(repairable,acceptable),(repairable,scrapped),(repiarable,repairable),(scrapped,acceptable),(scrapped,repairable),(scrapped,scrapped) 8. A sample of 2000 licensed drivers revealed the following number of speeding violations. Number of Violations Number of Drivers 0 1910 1 46 2 18 3 12 4 9 5 or more 5 Total 2000 a) What is the experiment? b) List the possible event. c) What is the probability that a particular driver had exactly two violations? d) What concept of probability does this illustrate? a) Each of the 2000 licensed driver were asked to record their accident for some period. b) The possible event is one of the 2000 drivers was asked to record the accident for some period. c) P (2) = 18/2000 = 0.009 d) The concept of illustrates the number of times event occurs divided by number of possible occurrences. 12. Solve the following: a) 20!/17! b) 9P3 c) 7C2 a) 20!/17! = [20 x 19 x 18 x 17 x 16 x ...... x 1] / [17 x 16 x 15 x ...... x 1] = 20 x 19 x 18 = 6840 b) 9P3 = 9!/(9 – 3)! = 9!/6! = 9 x 8 x 7 = 504 [ nPr = n! / (n – r)!] c) 7C2 = 7! / 2!(7 – 2)! = 7! / 2! 5! = (7 x 6) / 2 = 21 [nCr = n! / r! (n – r)! ] 20. The events X and Y are mutually exclusive. Suppose P(X) = .05 and P(Y) = .02. What is the probability of either X or Y occurring? What is the probability that neither X nor Y will happen? P (X or Y) = P (X) + P (Y) = 0.05 + 0.02 = 0.07 P (neither X nor Y) = 1 – P (X or Y) = 1 – 0.07 = 0.93 28. A student is taking two courses, history and math. The probability the student will pass the history course is .60, and the probability of passing the math course is .70. The probability of passing both is .50. What is the probability of passing at least one? We have P (history) = 0.60, P (math) = 0.70 and P (both) = 0.50 P (at least one) = P (history) + P (math) – P (both) = 0.60 + 0.70 – 0.50 = 0.80 36. Three defective electric toothbrushes were accidentally shipped to a drugstore by Cleanbrush Products along with 17 non-defective ones. a) What is the probability the first two electric toothbrushes sold will be returned to the drugstore because they are defective? b) What is the probability the first two electric toothbrushes sold will not be defective? a) P (first two defective) = 3/20 + 2/19 = 6/380 =0.01579 b) P (first two non-defective) = (17/20) + (16/19) = 272/380 = 0.7158 48. Berdines Chicken Factory has several retail stores. When interviewing applicants for server positions, the owner would like to include information on the amount of tip a server can expect to earn per check (or bill). A study of 500 recent checks indicated the server earned the following tips. Amount of Tip ($) Number $0 to under $5 200 5 to under 10 100 10 to under 20 75 20 to under 50 75 50 or more 50 Total 500 a) What is the probability of a tip of $50 or more? b) Are the categories “$0 to under $5”, “5 to under 10”, and so on considered mutually exclusive? c) If the probabilities associated with each outcome were totaled, what would the total be? d) What is the probability of a tip of up to $10? e) What is the probability of a tip of less than $50? a) P (tip 50 or more) = 50/500 = 0.10 or 10% b) Yes, because given tip cannot fall in more than one category. c) P (total) = 1 d) P (tip up to $10) = 300/500 = 0.60 or 60% e) P (tip less than $50) = 450/500 = 0.90 or 90% 74. A survey of Undergraduate Students in the School of Business at Northern University revealed the following regarding the gender and majors of students: Major Gender Accounting Marketing Finance Total Male 100 150 50 300 Female 100 50 50 200 Total 200 200 100 500 a) What is the probability of selecting a female student? b) What is the probability of selecting a finance or accounting major? c) What is the probability of selecting a female or an accounting major? Which rule of addition did you apply? d) What is the probability of selecting an accounting major, given that the person selected is male? e) Suppose two students are selected randomly to attend a lunch with the president of the university. What is the probability that both of those selected are accounting majors? a) P (female) = 200/500 = 0.40 b) P (F or A) = P (F) + P (A) = 100/500 + 200/500 = 300/500 or 0.6 c) P (female or A) = P (female) + P (A) – P (female and A) = 200/500 + 200/500 -100/500 = 300/500 or 0.6 d) P (A/male) = P (A and male)/ P (male) = (100/500)/ (300/500) = 100/300 or 0.33 e) P (both accounting) = (200/500)2 = 4/25 or 0.16 84. a) Some Saskatchewan license plates have three letters and three numbers. How many license plates of this type can there be? b) Some Ontario license plates have four letters and three numbers. How many license plates of this type can there be? a) There are total 26 letters and 10 numbers. Number of license plates = 263 x 103 = 17576 x 1000 = 17,576,000 b) There are total 26 letters and 10 numbers. Number of license plates = 264 x 103 = 456976 x 1000 = 456,976,000 88. A case of 24 cans contains 1 can that is contaminated. Three cans are to be chosen randomly for testing. a) How many different combinations of three cans could be selected? b) What is the probability that the contaminated can is selected for testing? a) 24C3 = 2024 b) =1* 2 C1 / 24C3 = 2/2024