4. (5 points) You are driving the speed limit on a very fast highway, 90% of dri

Question

4. (5 points) You are driving the speed limit on a very fast highway, 90% of drivers on this road exceed the speed limit by 20 MPH or more. 5% speed by less than 20 MPH over the limit, and 5% don't speed. A car speeds past you just as you reach a speed trap, at which it is known that 70% of drivers who are going 20 MPH or more or the limit are pulled over, and 20% of cars who are going 1-19.999 MPH over the limit are pulled over. The cops don't pull over non-speeders. You were driving at exactly the speed limit when a car passes you. What is the probability that the car which is passing you will be pulled over?

Explanation / Answer

P(that car which is passing you will be pulled over)=P(exceed 20MPH and pulled over)+P(exceed 1-19.99MPH and pulled over)=0.9*0.7+0.05*0.20=0.64

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