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04 STAT HWB q probability

# 04 STAT HWB q probability - Dr V.R Bencivenga Economics 329...

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Dr. V.R. Bencivenga Economics 329 PRACTICE HOMEWORK #4B: PROBABILITY THEORY 1. All components leaving an assembly line are examined by two inspectors. Each inspector detects 85% of defective components (in other words, given that a component is defective, the probability is .85 that an inspector will detect this). 80% of defective components are detected by both inspectors. What is the probability that a defective component will be detected by at least one inspector? 2. A survey of subscribers to Fortune Magazine found that in the past 12 months, 54% rented a car for business reasons, 51% rented a car for personal reasons, and 72% rented a car for personal or business reasons. a. What is the probability that a subscriber rented a car for business and personal reasons? b. Are the two events “rents a car for personal reasons” and “rents a car for business reasons” statistically independent? c. What is the probability that a subscriber did not rent a car in the last 12 months? d. What is the probability that an individual rented a car in the last 12 months for business reasons only? 3. A country wants to mount a military strike in retaliation against a terrorist group. This group hides its headquarters and practice sites in remote locations. The basic plan is to secretly position troops to seal off the area and mount the attack, and then strike the location with missiles just before the ground attack. In order for a strike against a terrorist location to succeed, the military must have the correct intelligence (i.e., the terrorists must be in the location at the chosen point in time); military transports must move troops and helicopters to a nearby staging area without being detected; battleships with cruise missiles must move offshore without being detected; helicopters must deliver the troops to their secret positions; and enough missiles must get through the terrorists’ missile defenses at the time the ground attack is initiated. Suppose that the probability of having the correct intelligence is 90%. The probability of moving troops and helicopters to the staging area without being detected is 80%. The probability of the getting the battleships into position offshore without being detected is 70%. Given that the troops and helicopters make it to the staging area without being detected, the probability is 75% that the troops can be delivered to their secret positions. Given that the battleships get into position without being detected, the probability is 95% that enough missiles will get through before the ground attack is initiated. The strike does not proceed unless it is the case that the troops and helicopters have been moved to the staging area without being detected, and the battleships have been moved into position without being detected. (I.e., unless this is the case, there is no attempt to deliver the troops to their secret positions, or to fire missiles. The attempt at a strike is halted and the strike is considered a failure.)

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04 STAT HWB q probability - Dr V.R Bencivenga Economics 329...

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