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 90% of the time; that is, there is a
0.90 probability that the gun will detect a speeder, if the driver
is actually speeding. Assume there is a 1% chance that the gun
erroneously detects a speeder even when the driver is below the
speed limit. Suppose that 96% of the drivers drive below the speed
limit on this stretch of the Massachusetts Turnpike.
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.)