2.102- Police plan to enforce speed limits byusing radar traps at 4 differrent l

Question

2.102- Police plan to enforce speed limits byusing radar traps at 4 differrent locations.The radar traps at eachof the locations L1, L2,L3 andL4 are operated 40 %,30%,20% and 30% of the time,and if a person who is speedingon his way to work hasprobabilities of 0.2 ,0.1, 0.5 and 0.2, respectively, of passingthrough these locations.What is the probability that he willreceive a speeding ticket ?
, 2.102- Police plan to enforce speed limits byusing radar traps at 4 differrent locations.The radar traps at eachof the locations L1, L2,L3 andL4 are operated 40 %,30%,20% and 30% of the time,and if a person who is speedingon his way to work hasprobabilities of 0.2 ,0.1, 0.5 and 0.2, respectively, of passingthrough these locations.What is the probability that he willreceive a speeding ticket ?
,

Explanation / Answer

So a good way to think is to ask what is the probability thathe doesn't get a speeding ticket and then subtract this from1.
P(he doesn't get caught by L1)=1-P(he gets caught at L1) =40%*0.2 = 1-8% = 92% P(he doesn't get caught by L2)=1-P(he gets caught at L2) =30%*0.1 = 1-3%=97% P(he doesn't get caught by L3)=1-P(he gets caught at L3) =20%*0.5 = 1-10%=90% P(he doesn't get caught by L4)=1-P(he gets caught at L4) =30%*0.2 = 1-6%=94%
P(he doesn't get caught) = P(he doesn't get caught at L1)*P(hedoesn't get caught at L2)*P(he doesn't get caught at L3)*P(hedoesn't get caught at L4)= 92%*97%*90%*94%= 75.4970%
therefore probability that he gets a speeding ticket = 1-75.4970 % = 24.5030%
Hope this helps you. Feel free to ask for anyclarifications

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.