Question
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A company makes electronic gadgets. They estimate that 3 out of every 100 gadgets
is faulty, but the company doesn’t know which ones are faulty until a buyer
complains. Suppose the company makes a profit on the sale of any working
gadget, but suffers a loss of for every faulty gadget because they have to repair
the unit. Check whether the company can expect a profit in the long term.
Find the expected profit per gadget.
Round your answer to two decimal places.

Ask by Moran Conner. in China
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The company can expect a loss of $0.46 per gadget in the long term.

Solution

To determine whether the company can expect a profit in the long term, we need to calculate the expected profit per gadget. We can do this by considering the probabilities of selling a working gadget and a faulty gadget, along with their respective profits and losses.

Step 1: Define the probabilities

  • Probability of a working gadget (not faulty):
  • Probability of a faulty gadget:

Step 2: Define the profits and losses

  • Profit from a working gadget:
  • Loss from a faulty gadget:

Step 3: Calculate the expected profit

The expected profit can be calculated using the formula:
Substituting the values we have:
Now, let’s calculate this step by step.
  1. Calculate the profit from working gadgets:
  2. Calculate the loss from faulty gadgets:
  3. Combine these results to find the expected profit:

Conclusion

The expected profit per gadget is . This means the company can expect a loss of per gadget in the long term.
Now, I will round the answer to two decimal places:
Thus, the company cannot expect a profit in the long term.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

Beyond the Answer

To find the expected profit per gadget, we can calculate the expected profit for both working gadgets and faulty gadgets based on their probabilities.
  1. The probability of a gadget being working is and the profit from a working gadget is .
  2. The probability of a gadget being faulty is , and the loss from a faulty gadget is .
Now, we calculate the expected profit per gadget:
Rounding to two decimal places, the expected profit per gadget is . This means that in the long term, the company can expect a loss of for each gadget produced.

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