Name: UoS ID: ON05) The four attendants of gasoline service station are of custo

Question

Name: UoS ID: ON05) The four attendants of gasoline service station are of customers' car. Jack, who services 20% of all cars, fails to wash the windshield one time in 20. Tom, who services 60% of all cars, fails to wash the windshield one time in 10, Gurgs who services 15% of all cars, fails to wash the windshield one time in 10, and Peter, who services 5% of all cars, fails to wash the windshield one time in 20. If a customer complains later that the windshield was not washed, what is the probability that her car was serviced by Jack? (05 Marks)

Explanation / Answer

there are four person here.

Pr(Jack will wash windshield) =20 % = 0.20

Pr(Fail to wash windshield l Jack wash the windshield) = 1/20 = 0.05

Pr(Tom will wash windshield) = 60%= 0.60

Pr(Fail to wash windshield l Jack wash the windshield) = 1/10 = 0.10

Pr(George will wash windshield) = 15%= 0.15

Pr(Fail to wash windshield l George wash the windshield) = 1/10 = 0.10

Pr(Peter will wash windshield) = 5% = 0.05

Pr(Fail to wash windshield l Peter wash the windshield) = 1/20 = 0.05

Pr(Fail to wash windshield) = 0.20 * 0.05 + 0.60 * 0.10 + 0.15 *0.10 + 0.05 * 0.05 = 0.0875

So,

Pr(Jack washed the windshield l Fail to wash windshield) = 0.20 * 0.05/ 0.0875 = 0.1143

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