The state police are trying to crack down on speeding on a particular section of

Question

The state police are trying to crack down on speeding on a particular section of a highway. To aid in this pursuit, they have purchased a new radar gun that promises greater consistency and reliability. Specifically, the gun will detect a speeder 98 percent of the time if the driver is speeding. The gun may also detect a driver as a speeder 1 percent of the time when the driver is not speeding. Suppose that 95 percent of the drivers drive below the speed limit on this section of the highway.

A) What is the probability that a driver on this highway will be a speeder and will not be detected by the radar gun? Show your work.                                           

B) Suppose the police stop a driver because the gun detects speeding. What is the probability that the driver was actually driving below the speed limit? Show your work.                                                                                         

C) What is the probability that a driver will be detected by the radar gun on this highway? Briefly explain/show how you arrived at your answer.   

D) What is the probability that a driver will be neither a speeder nor will be detected by the radar gun on this highway? Show your work.                                    

Explanation / Answer

Given Probabilities are:

P(True Over Speeder) = 0.05

P(False Over Speeder) = 0.95

P(True Over Speeder Detected) = 0.98

P(False Overspeeder Detected) = 0.01

P(True Non Overspeeder) = 0.99

P(False Non Over Speeder) = 0.02

since the two events are independent

A. What is the probability that a driver on this highway will be a speeder and will not be detected by the radar gun

P(True Over Speeder) * P(False Non Over Speeder) =  0.05 * 0.02 = 0.001

B. P(False Over Speeder) *  P(False Overspeeder Detected) = 0.95 * 0.01 = 0.095

C. P(True Over Speeder) = 0.05 *P(True Over Speeder Detected) = 0.05 * 0.98 = 0.0490

D. P(False Over Speeder) * P(True Non Overspeeder) = 0.95 * 0.99 = 0.9405

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