MA2212 - HW02

MA2212 - HW02 - Department of Mathematics Name Poly ID...

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Department of Mathematics Name: ________________________________ Poly ID: _______________________________ Instructor’s Name:_______________________ Course No:_____________________________ Course Section: _________________________ Homework Section No:___________________

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Willis Thai MA2212 HW02 1.3-1 A boy found a bicycle lock for which the combination was unknown. The correct combination is a four-digit number, d 1 d 2 d 3 d 4 , where d i , I – 1, 2, 3, 4, is selected from 1, 2, 3, 4, 5, 6, 7, 8. How many different lock combinations are possible with such a lock? 8 4 = 4096 1.3-5 How many four-letter code words are possible using the letters in HOPE if: (a) The letters may not be repeated? 4! = 24 (b) The letters may be repeated? 4 4 = 256 1.3-13 A café lets you order a deli sandwich your way. There are 6 choices for bread, 4 choices for meat, 4 choices for cheese, and 12 different garnishes (condiments). How many different sandwich possibilities are there if you choose: (a) One bread, one meat, and one cheese? 6 x 4 x 4 = 96 (b) One bread, one meat, one cheese, and from 0 to 12 garnishes? 6 x 4 x 4 x 2 12 = 393,216 (c) One bread; 0, 1, or 2 meats; 0, 1, or 2 cheeses; and from 0 to 12 garnishes? 6 x (1 + 4 + 4 C 2 ) (1 + 4 + 4 C 2 ) x 2 12 = 2,973,696 1.3-15 Among nine presidential candidates at a debate, three are Republicans and six are Democrats. (a) In how many different ways can the nine candidates be lined up? 9! = 362,880 (b) How many lineups by party are possible if each candidate is labeled either R or D ? 9 C 3 = 84 1.3-19 There are three teams in a cross country race. Team A has 5 runners, team B had 6 runners, and team C has 7 runners. In how many ways can the runners cross the finish line if we are only interested in the team for which they run? That is, what is the number of distinguishable permutations of 5 A’s, 6 B’s, and 7 C’s? (Note that for scoring purposes, only the scores of the first 5 runners for each team count.) ଵ଼Ǩ ହǨ଺Ǩ଻Ǩ = 14,702,688 1.4-1 A common test for AIDS is called the ELISA (Enzyme-Linked Immunosorbent Assay) test. Among 1,000,000 people who are given the ELISA test, we can expect results similar to those given in the table.
Willis Thai MA2212 HW02 If one of these 1,000,000 people is selected randomly, find the following probabilities: (a) P(B 1 ) = ହ଴଴଴ ଵ଴଴଴଴଴଴ = .005 (b) P(A 1 ) = ଻଼ହଵହ ଵ଴଴଴଴଴଴ = .079 (c) P(A 1 |B 2 ) = ଻ଷ଺ଷ଴ ଽଽହ଴଴଴ = .074 (d) P(B 1 |A 1 ) = ସ଼଼ହ ଻଼ହଵହ = .062 (e) In words, what do parts (c) and (d) say? Part (c) asks for the probability that a person will test positive if he/she does not carry the virus

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