The management of First American Bank was concerned about the potential loss that might occur in the event of a physical catastrophe such as a power failure or a fire. The bank estimated that the loss from one of these incidents could be as much as $100 million, including losses due to interrupted service and customer relations. One project the bank is considering is the installation of an emergency power generator at its operations headquarters. The cost of the emergency generator is $800,000, and if it is installed, no losses from this type of incident will be incurred. However, if the generator is not installed, there is a 10% chance that a power outage will occur during the next year. If there is an outage, there is a .05 probability that the resulting losses will be very large, or approximately $80 million in lost earnings.
Alternatively, it is estimated that there is a .95 probability of only slight losses of around $1 million. Using decision tree analysis, determine whether the bank should install the new power generator.