1. 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 98% of the time; that is, there is a 0.98 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 95% 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.)
Probability
b. What is the probability that the gun detects speeding and the driver was not speeding? (Round your answer to 4 decimal places.)
Probability
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?
2. Apparently, depression significantly increases the risk of developing dementia later in life (BBC News, July 6, 2010). In a recent study it was reported that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not have depression. Suppose 10% of all people suffer from depression.
a. What is the probability of a person developing dementia? (Do not round intermediate calculations. Round your answer to 3 decimal places.)
b. If a person has developed dementia, what is the probability that the person suffered from depression earlier in life?