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Problem 8. Suppose you are QC inspector for the Lucky Coin® company, who make specialized coins for flipping. Their main product is a coin that is supposed to come up heads 75% of the time. However, the machinery occasionally malfunctions without warning, producing a coin with probability of heads only 50%. To attempt to sort out the good coins from the defective ones, you implement the following QC policy: flip each coin five times and discard it if it doesn't come up heads at least three times (otherwise pass it). a) What is the probability of discarding good coins? b) What is the probability of passing defective coins? c) If your process is known to produce 20% defective coins, what fraction of coins that were discarded are actually good?

Problem 8. Suppose you are QC inspector for the Lucky Coin® company, who make specialized coins for flipping. Their main product is a coin that is supposed to come up heads 75% of the time. However, the machinery occasionally malfunctions without warning, producing a coin with probability of heads only 50%. To attempt to sort out the good coins from the defective ones, you implement the following QC policy: flip each coin five times and discard it if it doesn't come up heads at least three times (otherwise pass it). a) What is the probability of discarding good coins? b) What is the probability of passing defective coins? c) If your process is known to produce 20% defective coins, what fraction of coins that were discarded are actually good?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Problem 8. Suppose you are QC inspector for the Lucky Coin® company, who make specialized coins for flipping. Their main product is a coin that is supposed to come up heads 75% of the time. However, the machinery occasionally malfunctions without warning, producing a coin with probability of heads only 50%. To attempt to sort out the good coins from the defective ones, you implement the following QC policy: flip each coin five times and discard it if it doesn't come up heads at least three times (otherwise pass it). a) What is the probability of discarding good coins? b) What is the probability of passing defective coins? c) If your process is known to produce 20% defective coins, what fraction of coins that were discarded are actually good? d) If your costs are $5 for each defective coin passed and $2 for each good coin discarded, what is the cost of this QC policy on a per-item-produced basis? e) Relate the problem here to the discussion of diagnostic testing in the "conditional probability examples" notes. f) Find a cheaper QC policy (using the same flip-five-times test), if there is one. If not, explain why.
Transcribed Image Text:Problem 8. Suppose you are QC inspector for the Lucky Coin® company, who make specialized coins for flipping. Their main product is a coin that is supposed to come up heads 75% of the time. However, the machinery occasionally malfunctions without warning, producing a coin with probability of heads only 50%. To attempt to sort out the good coins from the defective ones, you implement the following QC policy: flip each coin five times and discard it if it doesn't come up heads at least three times (otherwise pass it). a) What is the probability of discarding good coins? b) What is the probability of passing defective coins? c) If your process is known to produce 20% defective coins, what fraction of coins that were discarded are actually good? d) If your costs are $5 for each defective coin passed and $2 for each good coin discarded, what is the cost of this QC policy on a per-item-produced basis? e) Relate the problem here to the discussion of diagnostic testing in the "conditional probability examples" notes. f) Find a cheaper QC policy (using the same flip-five-times test), if there is one. If not, explain why.
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