It is possible to answer this question by just looking at the values and their probabilities, though the correct answer can also be calculated. The alternative with the highest expected value will be the one where the higher values have higher probabilities. In Alternatives #1 and #2, a total of 70% probability is represented by values of $100,000 and $150,000. That is in contrast to Alternatives #3 and #4, where 70% probabilities are represented by $100,000 and $125,000 and $75,000 and $50,000, respectively. So we can determine that the highest expected value will be with either Alternative #1 or Alternative #2. We can see that in Alternative #2, the lower of the two values, $100,000, has a higher probability of occurring than it does in Alternative #1. And in Alternative #1, the higher of the two values, $150,000, has a higher probabiity of occurring than it does in Alternative #2. Since the probabilities of values of $50,000 and $75,000 are exactly the same for both alternatives, we can determine that Alternative #1 will have a higher expected value (weighted average) than Alternative #2. Or, we can calculate the expected value of each of the four alternatives and determine the highest of the four: Alternative #1: (.10 × $50,000) + (.20 × $75,000) + (.40 × $100,000) + (.30 × $150,000) = $105,000. Alternative #2: (.10 × $50,000) + (.20 × $75,000) + (.45 × $100,000) + (.25 × $150,000) = $102,500. Alternative #3: (.10 × $50,000) + (.20 × $75,000) + (.40 × $100,000) + (.30 × $125,000) = $97,500. Alternative #4: (.10 × $150,000) + (.20 × $100,000) + (.40 × $75,000) + (.30 × $50,000) = $80,000. The alternative with the highest expected value is Alternative #1.
This alternative cannot have the highest expected value because its highest cash flow is lower than that of some other alternatives, whereas the probability of its highest cash flow is similar to other alternatives.
This alternative cannot have the highest expected value because its probabilities of the higher cash flows are lower than its probabilities of higher cash flows.
This alternative cannot have the highest expected value because its probability of the highest cash flow is the lowest, whereas its probability of the second highest cash flow is the highest.
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