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A company makes electronic gadgets. 2% are faulty, the company doesn't know which ones are faulty until a buyer complains. Suppose the company makes a $21 profit on each sale, but has to refund the sale price and suffers a loss of $8 for every faulty gadget because they have to repair the unit. What is the profit(or loss) the company can expect to make from selling 100 units?
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Expected faulty units = 2% of 100 = 2 (on average).
Non-faulty units = 98.
Profit from each non-faulty sale = +\$21, loss for each faulty = refund + repair = -(21 + 8) = -\$29.
Total expected profit = 98(21) + 2(-29) = 2058 - 58 = \$2000.
(Equivalently, expected profit per unit = 0.98·21 + 0.02·(-29) = \$20, so for 100 units = \$20·100 = \$2000.)
Non-faulty units = 98.
Profit from each non-faulty sale = +\$21, loss for each faulty = refund + repair = -(21 + 8) = -\$29.
Total expected profit = 98(21) + 2(-29) = 2058 - 58 = \$2000.
(Equivalently, expected profit per unit = 0.98·21 + 0.02·(-29) = \$20, so for 100 units = \$20·100 = \$2000.)
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