TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/1.6

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Computer reliability

A campus bookstore sells two types of computers: laptops and desctops. In the last semester it sold 56% laptops and 44% desktops. Reliability rates for the two types of machines are quite different. In the first year, 5% of desktops require service, while 15% of laptops have problems requiring service.

(a) Sketch a probability tree for this situation.
(b) What percentage of computers sold by the bookstore last semester required service?
(c) Given that a computer required service, what is the probability that it was a laptop?

Lösungsvorschlag von Gittenburg[Bearbeiten | Quelltext bearbeiten]

--Gittenburg 09:41, 15. Okt. 2019 (CEST) a)

             computer
        0.56/        \0.44
       laptop         desktop
     0.15/  \0.85   0.95/ \0.05
  service    no service    service

b) 0.56 * 0.15 + 0.44*0.05 = 0.106

c) (0.15 * 0.56)/(0.15 * 0.56 + 0.44*0.05) ~= 0.79