Hi! if possible please show work/path you took so I can try and recreate the oth

Question

Hi! if possible please show work/path you took so I can try and recreate the other problems on my own

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 66% of the time; that is, there is a 0.66 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 63% of the drivers drive below the speed limit on this stretch of the Massachusetts Turnpike.

Explanation / Answer

To get such a question, you must have studied Bayes' rule.

a.
What is the probability that the gun detects speeding and the driver was speeding? (Round your answer to 4 decimal places.)
= (1 - .63) * 0.66

=0.2442

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

=0.01*0.63

=0.0063


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.)

=0.0063/(0.0062+0.2442)

= 0.02515

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