The Three attendants of gasoline service station are supposed to wash the windsh

Question

The Three attendants of gasoline service station are supposed to wash the windshield of each customer’s car. Jack who services 20% of all cars, fails to wash the windshield 10% of time. Tom, who services 50% of the cars, fails to wash the windshield 14% of time. George, who services 30% of cars, fails to wash the windshield 20% of time.

a) What is the probability a windshield of a customer’s car will not be washed?

B1- Jack services 20% of carsP(B1)=0.20P(F|B1)= 0.10

B2-Tom services 50% of carsP(B2)=0.50P(F|B2)=0.14

B3- George Services 30% of carsP(B3)=0.30P(F|B3)=0.20

F- Fails to wash wind shieldP(F)=?

SO,

P(F)= P(F|B1)*P(B1)+ P(F|B2)*P(B2)+ P(F|B3)*P(B3) =0.15

P(F’)=1-.15=.085

b) If Jackie finds that her car windshield is not washed what is the probability that her car was serviced by Tom?

P(B2|F) = [P(F|B2)*P(B2)]/[ P(F|B1)*P(B1)+ P(F|B2)*P(B2)+ P(F|B3)*P(B3)]= 7/15

c) What is the probability a selected car was not serviced by Tom and windshield was not washed?

P(B2’|F)= 1-P(B2|F)= 8/15

d) What is the probability that a car was serviced by Jack and windshield was washed?

P(B3|F’)=P(B3 union F’) /P(F’) =24/85

Note: These are the answers I calculated, can you please explain them if any of these are incorrect?

Thank You!

Explanation / Answer

Let

J, T, G = jack, tom, george
W = fails to wash the windshield

Hence

a)

P(W) = P(J) P(W|J) + P(T) P(W|T) + P(G) P(W|G)

= 0.20*0.10 + 0.50*0.14 + 0.30*0.20

= 0.15 [ANSWER]

****************

B)

P(T|W) = P(T) P(W|T)/P(W) = 0.50*0.14/0.15 = 0.466666667 [ANSWER]

*********************

C)

P(T' n W) = P(J) P(W|J) + P(G) P(W|G)

= 0.20*0.10 + 0.30*0.20

= 0.08 [ANSWER]

*****************

D)

P(J n W') = P(J) P(W'|J) = 0.20*(1-0.10) = 0.18 [ANSWER]

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