Question

The State Police are trying to crack down on speeding on a particular portion of the Massachusetts Turnpike. To aid in this pursuit, they have purchased a new radar gun that promises greater consistency and reliability. Specifically, the gun advertises ± one-mile-per-hour accuracy 85% of the time; that is, there is a 0.85 probability that the gun will detect a speeder, if the driver is actually speeding. Assume there is a 2% chance that the gun erroneously detects a speeder even when the driver is below the speed limit. Suppose that 82% of the drivers drive below the speed limit on this stretch of the Massachusetts Turnpike. Hint: A probability tree might be helpful here.

a. What is the probability that the gun detects speeding and the driver was speeding? (Round your answer to 4 decimal places.)

b. What is the probability that the gun detects speeding and the driver was not speeding? (Round your answer to 4 decimal places.)

c. 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? (Round your answer to 4 decimal places.)

Answer 1

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