Question
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.
is faulty, but the company doesn’t know which ones are faulty until a buyer
complains. Suppose the company makes a
gadget, but suffers a loss of
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.
-
Calculate the profit from working gadgets:
-
Calculate the loss from faulty gadgets:
-
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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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.
- The probability of a gadget being working is
and the profit from a working gadget is . - 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.