Question

Question 3 (13 marks) Your online wine company, Vinophile, has three different employees that make sales calls. Employee A works 50% of shifts (mostly weekdays) and makes sales on 15% of their calls. Employee B works 40% of shifts (some week days and weekends) and makes sales on 20% of their calls. Employee C works 10% of shifts (mostly weekends) and makes sales on 30% of their calls. a) Present this information in a fully labelled tree diagram that shows marginal, conditional and joint probabilities. (6 marks) b) What proportion of calls result in sales? (3 marks) c) Given that a sale is made, what is the probability that the call was made by employee A, B or C? (3 marks) d) Which employee is the best salesperson? If you think it is not possible to tell explain why. (1 mark)

Answer 1

(0.4 B & let E Event that an employee make sells on his her calls. PA) PA): 0.5, PCB) = 0.4, PC02001 P(A):0.15 , P(78)=0-20, PCE%c)-0.30 9.15E PLANE)= 0.5*0.15=0.075 10.85, Ē Plane -0.5*0.8570.425 0.20 € POBNE)20.4.0.220.08 0.80>Ē Pione): 0.408 -0.32 puogo, E PLENE)20.1*0.320.03 e-L0.70 Ē Plene) = 0.1*0.720.07 O DIE) Plane)+( BE) HP(ene): 0.185 = 18,5% © P9 Pl9E)= PLADE), 0.075 -0.4054= 40.54% ET DOET 0.185-O P(Ble): PCBNE), 0.080 :0.4324 = 43.24% PLE) - d. 185 P(4e), Pene).0.030 - 0.16221622% PLE) 00185 D Employee c is best sales person as hecan convert maximum calls he made to sell (30%)

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