The State Police are trying to crack dow n on speeding on a particular portion o f 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-m ile-per-hour accuracy 98% o f the tim e; th a t is, there is a 0.98 probability that the gun w ill detect a speeder, if the driver is actually speeding. Assume there is a 1% chance that the gun erroneously detects a speeder even w hen the driver is below the speed lim it.

Suppose th a t 95% o f the drivers drive below the speed lim it on this stretch o f the Massachusetts Turnpike.

a. W hat is the probability th a t the gun detects speeding and the driver was speeding?

b. W hat is the probability th a t the gun detects speeding and the driver was not speeding?

c. Suppose the police stop a driver because the gun detects speeding. W hat is the probability that the driver was actually driving below the speed limit?  P-258