Steve, a student at SJSU, has illegally parked his car in the employee parking l

Question

Steve, a student at SJSU, has illegally parked his car in the employee parking lot. If Robert the ticket-writer is on duty there’s a 90% chance that Steve will get a ticket because of Robert’s vigi- lance. If any other ticket-writer is on duty, there’s only a 50% chance that Steve will get a ticket. Steve doesn’t know which ticket-writer is on duty, but there’s a 30% chance that it is Robert.

(a) Define events that would be useful in analyzing this situation.
(b) Write out mathematically the probabilities that are provided as well as their complements.

(c) If Robert is on duty, what is the probability that Steve does not get a ticket?
(d) Using common sense, is the probability that Steve gets a ticket closer to 50% or 90%?

(e) Calculate the probability that Steve gets a ticket.

(f) It turns out that Steve was lucky and did not get a ticket. What is the probability that Robert was the ticket-writer on duty?

Explanation / Answer

Answer)

(A) Events are-

A: Steve will get a ticket

B: Robert, the ticket-writer, is on duty

C: Any other ticket writer is on duty

(b) P( Steve will get ticket/ Robert is on duty) =P(A/B)= 0.9

P(Steve will get ticket/Any other ticket-writer is on duty) = P(A/C) = 0.5

P(Robert is on duty) = 0.3

(c) P(Steve doesnot get ticket/ Robert is on duty) = P(Ac/B) = 1-P(A/B) = 1-0.9=0.1

(d) Using common sense, P(Steve gets ticket) is closer to 90%.

(e) P(Steve gets ticket) =P(A) = P(A/B) P(B) + P(A/C) P(C)

= 0.9*0.3 +0.5*(1-0.3) = 0.62

(f) P(Robert is on duty/ Steve didnot get ticket) = P(B/Ac)

= P(Ac/B)P(B)/ P(Ac)

= 0.1*0.3/(1-0.62) = 0.078

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