Robin, who travels frequently between two cities, has two route options: Route A is a fast four-lane highway, and route B is long winding road. The highway patrol has a limited police force. If the full force is allocated to route A or B, Robin, with her passionate desire for driving superfast, is certain to receive a $100 speeding ticket. If the force is split 50-50 between the two routes, the is a 50% change she will get the $100 ticket on route A and only 30% chance that she will get the same fine on route B. Develop strategy for both Robin and the police.
Answers
Answer:
Robin should choose route B since the chance of getting fined is less.
Police shouldn't split force since it reduces their probability of catching Robin.
Step-by-step explanation:
The chances of police allocation can be seen as follows,
All on Route A=1/3
All on Route B=1/3
50-50 split=1/3
Assuming Robin doesn't know which route has how much police force allocated to which route,
Robin's chance of getting fined on route A
= (1/3)(1) + (1/3)(0) + (1/3)(1/2)
= 1/3 + 1/6 = 0.5
Robin's chance of getting fined on route B
= (1/3)(0) + (1/3)(1) + (1/3)(3/10)
= 1/3 + 1/10 = 0.43
So, Robin should choose route B since the chance of getting fined is less.
The chances of Robin choosing a route can be seen as follows,
Route A=1/2
Route B=1/2
Assuming the police doesn't know which route Robin chooses,
Police's chance of fining with full force on route A
= (1/2)(1) = 0.5
Police's chance of fining with full force on route B
= (1/2)(1) = 0.5
Police's chance of fining with split force
= (1/2)(1/2) + (1/2)(3/10) = 0.4
So, Police shouldn't split force since it reduces their probability of catching Robin.