After observing the heavy snow that his town received the previous winter, Ajay Patel, an enterprising student, plans to offer a snow-clearing service in his neighborhood this winter. If he invests in a new heavy-duty blower, Ajay forecasts a profit of $700 if snowfall this winter is heavy, a profit of $200 if it is moderate, and a loss of $900 if it is light. As per the current weather forecasts, the probabilities of heavy, moderate, and light snowfall this winter are 0.4, 0.3, and 0.3, respectively.
Rather than purchase a new blower, Ajay could get his father’s blower repaired and just accept smaller jobs. Under this option, Ajay estimates a profit of $350 for a heavy snowfall, a profit of $100 for a moderate snowfall, and a loss of $150 for a light snowfall. Ajay, of course, has the option of choosing neither of these options.
The local weather expert, Samantha Adams, is Ajay’s good friend. For $50, she is willing to run sophisticated weather models on her computer and tell Ajay whether she expects this winter to be unseasonably cold. For the sake of solving this problem, assume that the following information is available. There is a 45% chance that Samantha will predict this winter to be unseasonably cold. If she does say this, the probabilities of heavy, moderate, and light snowfall are revised to 0.7, 0.25, and 0.05, respectively. On the other hand, if she predicts that this winter will not be unseasonably cold, these probabilities are revised to 0.15, 0.33, and 0.52, respectively.
Draw the decision tree for the situation faced by Ajay. Fold back the tree and determine the strategy you would recommend he follow. What is the efficiency of Samantha’s information?