The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. he estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows:
bus demand low medium high
small 50 60 70
medium 40 80 90
large 20 50 120
prior probability 0.3 0.3 0.4

what is the expected annual profit for the bus that he will decide to purchase using bayes’ decision rule?