IUT of Saint-Etienne Sales and Marketing department Mr Ferraris Prom /2017

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1 IUT of Sait-Etiee Sales ad Marketig departmet Mr Ferraris Prom /2017 MATHEMATICS 2 d semester, Test 2 legth : 2 hours coefficiet 1/2 Graphic calculators are allowed. Ay persoal sheet is forbidde. The presetatio ad the quality of your writigs will be take ito accout. Your rouded results must be expressed with at least four sigificat figures. Full ame : Group : B1 Exercise 1 : MCQ (2 poits) tick the right boxes below Oe correct aswer oly per questio - 0 poit i case of wrog/missig/multiple aswer at a questio 1) ( A B) ( A B)... A B A B A B 2) If Card ( A B) = Card ( A) Card ( B), the: A = B Card ( A B) = 2 Card ( B) Card ( A) Card ( B) = A ad B itersect 3) If two evets A ad B are idepedet, the: p(a) + p(b) = 1 p A (B) = p B (A) p(a B) = p(b) p A(B) = p A(B) 4) Which oe is the correct iequality? P C C P C P C P Exercise 2 : Cardial umbers (4 poits) A survey cosists i aalysig the sales quatities of two products a ad b i a shop. Withi 200 cliets, 57 bought the objet a, 103 bought the objet b, 38 bought both objects. We ame A the set of cliets who bought the object a ad B the set of cliets who bought the object b. Card A B ad the give a cocrete meaig of this umber. 1 pt 1) Calculate ( ) 2) Build a cotigecy table for A, B ad their cotraries. 1 pt S2 Mathematics TEST 2 page 1 / 6

2 3) Thaks to this table, say (justify your aswers ad ame the correspodig sets): a. How may people bought either a or b. 0.5 pt b. How may people bought exactly oe of both objects. 0.5 pt 4) What is the probability that a cliet bought the object b, give that this perso bought the object a. 1 pt Exercise 3 : Coutig (2 poits) Seve cadidates (A, B, C, D, E, F ad G) stad i muicipal electios. You will aswer the followig questios by justifyig the coutig tools used. 1) At the cout of the first roud, these cadidates are raked i descedig order of the umber of votes obtaied. How may differet rakigs are possible for these seve cadidates? 1 pt 2) Both cadidates who scored the best are qualified for the secod roud. How may differet secod rouds are possible? 1 pt S2 Mathematics TEST 2 page 2 / 6

3 Exercise 4 : Coutig ad probabilities (5 poits) A magicia shows a set of 32 playig cards (4 colours, 8 cards per colour: hearts, spades, clubs, diamods) to the audiece who oly sees the reverse side. 1) First game: the magicia asks perso A to pick a card at radom, memorise it, ad the put it back i the set he immediately mixes. He does the same with three other people B, C ad D. a. How may differet draws, i the order A, B, C, D, are possible? 0.5 pt b. What is the probability that A would pick a heart? 0.5 pt c. What is the probability that A would pick a heart ad B would pick a spade? 0.5 pt 2) Secod game: the magicia asks perso A to make a simultaeous draw of four cards. a. Calculate the umber of differet possible draws. 0.5 pt b. What is the probability that A would pick four clubs? 1 pt c. What is the probability that A would pick exactly two kigs? 1 pt S2 Mathematics TEST 2 page 3 / 6

4 d. How may possible draws would ow exactly two kigs ad two clubs? 1 pt Exercise 5 : Coditioal probabilities (3 poits) A territorial orgaizatio coducted a study i the arts ad crafts (fr: artisaat) sector. Its itetio is to allocate a subsidy (fr: subvetio) to craftspeople (fr: artisas) who request it, ad preferably to those who have a professioal developmet project ad who wish to carry it out. * 30 % of craftspeople really have such a project ad, amog them, 92% ask for a subsidy (ad will get it); * Amog the other 70%, oe fifth ask for a subsidy, will get it, but wo't carry some project out. If at least two thirds of the allocated subsidies will cotribute to real ad accomplished projects, the orgaizatio will cosider its "subsidy operatio" as a success. 1) Accordig to the results of the study, build, as you wish: a probabilistic choice tree or a cotigecy table (you may the choose a total umber of 1000 craftspeople). 1.5 pt 2) Calculate the probability that a craftsperso would carry his (or her) project out, give that the orgaizatio allocated a subsidy to him (or her). Ca the "subsidy operatio" be regarded as a success? 1,5 pt S2 Mathematics TEST 2 page 4 / 6

5 Exercise 6 : Radom variable (4 poits) A compay is used to maufacture three products A, B ad C, ad is forecastig its commercialisatio costs. A represets 20 % of the productio, B represets 45%, ad C represets 35 %. Typical commercialisatio costs, for each produced uit of A, B, or C, are i the same order: 30, 36, 42, except i 30 % cases (same for A, B, or C), where this cost rises by 6 (extra costs for exports). 1) Build a probabilistic choice tree that displays the six differet possible situatios of costs. 0.5 pt 2) Give the probability distributio of the variable X : "commercialisatio cost of a uit". 1 pt 3) What is the probability that X may exceed 40? 0.5 pt 4) Calculate the expectatio of X. Iterpret its value. 1 pt 5) Give a estimate of the commercialisatio cost of 5,000 produced uits, followig the iformatio give by the directios of this exercise. 1 pt TEST END S2 Mathematics TEST 2 page 5 / 6

6 S2 Mathematics TEST 2 page 6 / 6

SCHOOL OF ACCOUNTING AND BUSINESS BSc. (APPLIED ACCOUNTING) GENERAL / SPECIAL DEGREE PROGRAMME

All Right Reserved No. of Pages - 10 No of Questios - 08 SCHOOL OF ACCOUNTING AND BUSINESS BSc. (APPLIED ACCOUNTING) GENERAL / SPECIAL DEGREE PROGRAMME YEAR I SEMESTER I (Group B) END SEMESTER EXAMINATION