TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2020W/HW02.4

Computer reliability

A campus bookstore sells two types of computers: laptops and desktops. 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.

1. Sketch a probability tree for this situation.

2. What percentage of computers sold by the bookstore last semester required service?

3. Given that a computer required service, what is probability that it was a laptop?

Lösungsvorschlag von Friday

--Friday Sa 30 Jan 2021 14:32:05 CET

Part a)

Part b)

As one can see from the probability tree, there are only two paths that lead to a computer needing a service. The first one is if the computer is a laptop and needs service and the second one is, if the computer is a desktop and needs a service. So all we have to do now is to compute the probability of each path and then add them. (Which we are allowed to do since the two events are independent, as a Computer cannot be a desktop and a laptop.)

$$(0.56*0.15)+(0.44*0.05)=0.106\quad \Box$$

Part c)

To solve this problem we can devide the probability that a laptop requires service, by the probability that any computer needs a repair (which we calculated in part b).

$${\frac {0.56*0.15}{0.106}}\approx 0.79\quad \Box$$