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A company makes electronic gadgets. One out of every 50 gadgets is faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose the company makes a $3 profit on the sale of any working gadget, but suffers a loss of $80 for every faulty gadget because they have to repair the unit. Find the expected profit for the company, Then estimate their total profit if they sell 150,000 gadgets.

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Answer:

Expected value = $1.34

Estimated Profit = $201,000

Explanation:

Faulty gadget probability = 1/50

Faulty gadget value = -$80

Working gadget probability = 49/50

Working gadget value = $3

The expected profit for selling a gadget is given by multiplying the probability of a working gadget being sold by its associated profit and addingt it to the product of the probability of a faulty gadget being sold by its associated loss:

[tex]EV = \frac{49}{50}*\$3 +\frac{1}{50}*-\$80 \\EV= \$1.34[/tex]

If they sell 150,000 gadgets the total profit is:

[tex]P=150,000 *EV\\P=150,000*1.34\\P=\$201,000[/tex]

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