Expected Value of Profit per Laptop
Company XYZ generates a profit of 500 for each defective laptop. If 3 out of every 100 laptops produced are defective, calculate the expected value of profit per laptop.
In this problem, we are tasked with determining the expected value of profit per laptop, which involves understanding the concepts of expected value and probability in the realm of discrete random variables. The expected value is a fundamental concept in probability that provides a measure of the average outcome when an experiment is repeated many times. Here, the context is set in a business scenario where the company wants to evaluate its profitability considering both successful and defective products.
To solve this problem, you need to first identify the possible outcomes and their respective probabilities. There are two main outcomes: the occurrence of a profit when non-defective laptops are sold, and a loss when defective laptops are produced. By calculating the weighted average of these outcomes, considering the probability of each, you can derive the expected profit per laptop.
This exercise illustrates the practical application of probability in business settings and helps in assessing risk and expectations. By understanding how to calculate expected values, businesses can make informed decisions that may impact pricing strategies, production processes, and quality control. The use of expected value can also extend to other areas of statistics and is a stepping stone for more complex analyses in risk management and decision theory.
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