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A company makes cellular phones. One out of every $25$ phones are faulty, but the company doesn’t know which phones are faulty until a customer complains. Suppose the company makes a $ \$ 30$ profit on the sale of any working phone but loses $ \$ 800$ for every faulty phone because they must replace it.

I have this shown below, however, I am getting a negative number:

$$E(x)= \frac{24}{25} \cdot 30 + \frac{1}{25} \cdot-800$$

Toby Mak
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    It seems to me the question is posed as "can the company expect to make a profit" which means the answer can be yes or no, which will indeed depend on if the profit is positive or negative. So, getting a negative profit gives you the answer. In this case, to make a profit, the company would need to change its manufacturing process to make it either cheaper and/or more reliable. – Michael May 07 '20 at 04:12

1 Answers1

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There's nothing wrong with what you have done.

Take a simpler problem for example: calculate the expected value if I gain $1$ dollar for a head, and lose $2$ dollars for a tail. I am losing money on average, so how does the expected value tell me I am losing money?

Toby Mak
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