Question

Decision Tree

A professional sports team has estimated that the revenue it generates per season is dependent on the number of wins in that season. They assume that signing a new player will result in a higher number of wins. Management is considering hiring a sports agent at a cost of $1.2 million to assist with signing a new player.

If an agent is not hired and the team completes their season with the current roster then there is a 60% probability that the team generates 95 million and a 40% probability that it genereates 105 million.

If management decides to hire the sports agent to assist with the signing process. They then have 2 options,

1. Sign an established star for 12 million. This will result in a 65% probability that the team will make 155 million and a 35% probability that revenue will be 130 million.
2. Sign a rookie for 4.5 million. This will result in a 30% probability that the team will make 155 million and a 70% probability that revenue will be 125 million.

1. Draw the decision tree
2. Calculate the probabilities and find the best course of action for the team.

a. Draw the decision tree for this problem.     

b. Calculate the expected values and determine the best decision for the company.

Answer 1