Police plan to enforce speed limits by using radar traps at 4different locations

Question

Police plan to enforce speed limits by using radar traps at 4different locations within the city limits. The radar trapsat each of the locations L1, L2, L3, and L4 are operated40%, 30%, 20%, and 30% of the time, and if a person who is speedingon his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2,respectively, of passing through these locations,
(a) What is the probability that he will receive a speedingticket?
(b) The person received a speeding ticket on his way to work, whatis the probability that he passed through the radar trap located atL2?

I know I'm supposed to find the relation between the location, theoperating time and the probability of getting a ticket at thatlocation, but I am not sure how to. Any help would beappreciated, and rated. Thanks.

Explanation / Answer

a) The probability that he will recieve at least oneticket is equal to: P(recieves a ticket at L1) + P(...L2) +P(...L3) + P(...L4). The probability that he recieves a ticket at agiven location is expressed as:  probability that hepasses through the location * the probability that the police areoperating the trap at that time. So, the total probability that he recieves at least one ticketis: P(recieves a ticket at L1) + P(...L2) + P(...L3) + P(...L4) =(.2*.4)+(.1*.3)+(.5*.2)+(.2*.3) = .27 b) I'm not sure if you mean the probability that he passedthrough and recieved a ticket or if he passed through withoutgetting a ticket. I'm going to assume you mean the probability thathe got a ticket at L2 given that he got a ticket on his way towork. P(Pass through L2 and got a ticket | recieved a ticket) =(.1*.3)/.27 = .1111...

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