A company makes electronic doohickeys. Seventeen out of every 80 doohickeys are faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose a doohickey costs $33 to make and they sell it for $55. This means the company makes a $22 profit on the sale of any working doohickey, but suffers a loss of $75 for every doohickey that is faulty because they have an amazing guarantee and will repair the unit. How much is the expected value of each doohickey? Can the company expect a profit in the long term? How much profit will they make if they sell 100 doohickeys? How much overall profit will they make if they sell 2000?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2. A company makes electronic doohickeys. Seventeen out of every 80 doohickeys are faulty,
but the company doesn't know which ones are faulty until a buyer complains. Suppose a
doohickey costs $33 to make and they sell it for $55. This means the company makes a $22
profit on the sale of any working doohickey, but suffers a loss of $75 for every doohickey
that is faulty because they have an amazing guarantee and will repair the unit.
How much is the expected value of each doohickey? Can the company expect a profit in
the long term? How much profit will they make if they sell 100 doohickeys? How much
overall profit will they make if they sell 2000?
Transcribed Image Text:2. A company makes electronic doohickeys. Seventeen out of every 80 doohickeys are faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose a doohickey costs $33 to make and they sell it for $55. This means the company makes a $22 profit on the sale of any working doohickey, but suffers a loss of $75 for every doohickey that is faulty because they have an amazing guarantee and will repair the unit. How much is the expected value of each doohickey? Can the company expect a profit in the long term? How much profit will they make if they sell 100 doohickeys? How much overall profit will they make if they sell 2000?
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