MATH 204 Exam 2, Fall 2016

American University of Beirut Math 204 Quiz II — (Fall 2016) Time 60 minutes. Name: ID#: Circle your problem solving section number below: e Instructor: Ms Joumana Tannous Section 1 @ 1:00 M Section 2 @ 11:00 M Section 3 @ 4:00 M e Instructor: Mrs Maha Itani-Hatab Section 4 @ 11:00 Tu Section 5 @ 8:00 Tu Section 6 @ 12:30 Tu e Instructor: Ms. Michella Bou Eid Section 7 @ 12:30 Th Section 8 @ 2:00 Th Section 9 @ 5:00 Th e Instructor: Ms Najwa Fuleihan Section 10 @ 8:00 Tu Section 11 @ 2:00 Tu Section 12 @ 11:00 Tu Ye ot Pag DN Grade Me y /23 3 /25 4 /28 5 124 Total /100 1) To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 7 computers and one of 3 printers. How many possible computer systems a customer can choose? (3 pts) Ux2x4txKd 2) A committee of seven consisting of a chairman, a vice chairman, a secretary, and four other members is to be chosen from a class of 20 students. In how many ways can this committee be chosen? (4 pts) ° 20% x14Gy 3) Three-digit numbers are formed using the digits 2, 3, 4, 5, and 7. How many such numbers can be formed if the numbers are: i. greater than 700 and repetition is allowed? (8 pts) xox ii. even and repetition is not allowed? yx 3X2 iii. less than 700, divisible by 5 and repetition is not allowed? 3x3x4 4) The phone number of Jad is 03 386 350. How many different passwords can he form using the eight digits of his phone number? { (3 pts) pa, Lee 2igl ill 5) A company has 2844 employees. Is it possible to give each employee an ID number that consists of one letter followed by two digits? Explain. (5 pts) The numbe of waite to prim He TD to i nuntec of TDs <mumbee xf Hal } ” 6) Solveforn 2 ,,P,= 3,C, N23 In>% (7 pts) aad : (an)! ini so csniik lisa (n-3)J (2n-3) 1 3! ae BRE Zz on ln-1) (n-2) (n-a)=-4" = (in) lan-1) Cn-D Cn (naa) (nau) 22 = 24 (a 43 _o - BX2X/ nz (23) 6x darfn-1) (n-2) = Anlam-t) (nr) Beware Un-—-4n~m+d ) vite ee 6 (n*-3n42) = bn? -™- - 1) (n-5)20 ‘ dmt~ idu+ 1020 —- n*_ Ents 20 = ye He F accep h 7) Suppose that your street has two traffic lights. The chance that the first light is red is 0.4, (18 pts) the chance that the second light is red is 0.3 and the chance that both are red at the same time is 0.1. a. Draw a Venn diagram to represent the given. b. What is the probability that: i. _ the first or the second light are red? P ( L,U L2) 2 P (Li) +P(L2) = PCL Lx) hs Paros ee =z ii. _ the first light is red and the second light is not? P(L, Ali) = 03 iii. exactly one of the lights is red? : na On Sr P(t nti) + P(t, aL) = ©:3+0 iv. the second light is red given that the first light is red? PlL2[ Ls) = P(Urtz) =, Ost 5A p (Li) Ort 4 ce. Are the events “the first light is not red” and “the second light is not red” mutually exclusive? - ol a \ | P (Li ALi) = eliUts) 2 = 2) 20,440 oS - oo thay aw uot oct ley exclea'y d. Are the events “the first light is red” and “the second light is red” independent? P(uinta) = OI 8) A bag contains 2 red, 3 green and 4 blue balls. Two balls are drawn at random from the urn, what is the probability that none of the balls drawn is blue? (3 pts) 5 x U 4y C, K sC, _—_— © r “ 9 S a Ca 9) The probabilities that three different students A, B and C wi respectively 0.6, 0.7 and 0.8. Assuming independence. i. Find the probability that only one will get a scholarship. (5 pts) Or GxOw3xGiL +Oy xOFxOd + GU KD3xO8 _ Beg O.OBG + C°'056 + 01046 ii. _If only one got a scholarship, what is the probability that he is student A? PCR lonly one = O6xO.3x0.L = 0.14 ONES 10) In a restaurant seventy percent of people order only Chinese food and thirty percent order only Italian food. A group of three persons enter the restaurant, what is the probability that at least two of them order Italian food ill get a scholarship are Bp) P(XZ2) = e C2 (03) (ayaa, (03) (oay 11) The probability that a man will purchase sports cars is 0.6. If 10 sports car owners are randomly selected, find the probability that: (17 pts) i. exactly 7 are men. 3 POX =) = to ee (o.6)* (0-4) ii. exactly 5 are women a : P Cy=5) = 1 Ce (o ) (014) iii. at least 2 are men PC%7,2) =1- PCX=% we | — [i ie (0.6) (04) +00 ‘e (0:6) (ou) iv. between 4 and 6 are men z PCucx<s) = P(x=5) = Cy 6) (0-4) v. more than 7 men given that at most 9 are men te | P (x >+| X <4) - _Paxx<4a) = P(x=8,4) = iwCge6) Ctr Ca Od PCxea) 1 P(X=10) vi. no less than 8 are men 10 P(X 8) =PO=8,5,10) =, (Oflu re Gy CIE) + GulE e Ina sample of 120 sports cars owners, what is the expected number of men? Me AQNOxO-GaH 42. 12) The question “ Do you smoke? ” was asked to a sample of 100 people. The results are shown in the following table. One person is (24 pts) selected at random. B1 Male | Female | Total Smoker 16 3 9 Nonsmoker | 64 17 81 Total 80 20 100 oS Ss N a. Use the table to fill in the boxes of the tree diagram by the corresponding probabilities. Justify your answers ise sent pexBi: (sm) = PCsa) - i Ss Pim) = 16 = 9.% gD Box B2: aft 2) _ plnow) 2 44 209 (tr lo, N Box B3: p(sne) Is ajn\ . PISOEL = 4 29 P(s|F) = BLP) 20 E Box B4: (on j-O.15 = 0.85) -) . PIWAP) - 1% = 939 Pl vir) = Pia QD b. Find the probability that the selected person is: i. a female and nonsmoker P(FAN) = 5 20. IF ii. a male or smoker ee eee pim ys) = Pim) + Pls) - Ta aie ae iii. neither a male nor a smoker pimias') > Plmus) = )- PlAVS) = Bt c. If the selected person is nonsmoker, what is the probability that he is a male? M nv) = pPlMan) . Se = 0s 24 0/ p(M/ now) = d. Are the events “is nonsmoker” and “is a female” collectively exhaustive? = e/ 20 — Fh = PY 094 PIN UF) = PIN) + PLE) - PONOE) = 169 yo 100 100 5 PINVF) #1 — > NUF ¢ Sawfle Space