This is the expected payoff for selling soft drinks when the weather is cold multiplied by the probability of cold weather of .60, plus the expected payoff for selling coffee when the weather is hot multiplied by the probability of hot weather of .40. That is not the expected payoff for selling coffee.
This is the expected payoff for selling coffee when the weather is cold multiplied by the probability of cold weather of .60, plus the expected payoff for selling soft drinks when the weather is hot multiplied by the probability of hot weather of .40. That is not the expected payoff for selling coffee.
The beverage stand can sell either soft drinks or coffee on any given day ? not both. Since the question asks for the expected payoff for selling coffee, the proprietor is asking for the answer to this question: "Assuming I take coffee with me to sell today, what is my expected payoff for doing that?" Thus, the probability is 100% that coffee will be served. To solve this problem we have to identify the expected payoff of selling coffee when we know the probabilities of the weather being hot and cold. That will be the weighted average of the expected payoffs for serving coffee, weighted according to the probabilities of cold weather and hot weather. So we will multiply each possible payoff for selling coffee by its corresponding probability. If the stand sells coffee and the weather is hot, it will make $1,900, and the probability of hot weather is 40% (100% ? 60% probability of cold weather). If the stand sells coffee and the weather is cold, it will make $2,000, and the probability of cold weather is 60%. Thus, the weighted average profit for selling coffee is ($1,900 × .40) + ($2,000 × .60), which is $1,960. And that is the expected payoff for selling coffee.
This is not possible, as the maximum the beverage stand can obtain is $2,500 if it sells soft drinks when the weather is hot.
|
