Jen Johnrs, the owner of a restaurant, must decide whether to substantially expand the restaurant or settle for minor renovations. The decision is based on the population growth of the town. If the main employer in town cuts back on its workforce, the town's population may decrease. If new businesses can be attracted to the town, the population may increase slightly, or possibly, increase significantly.Jen Johnrs has constructed a payoff table with the possible returns for each action based on the state of nature. The probabilities for each state of nature are also presented.

States of Nature

ActionDecrease (D)Slight Increase (SI)Significant Increase (I)

Expand (a₁)$-14,000$21,000$ 36,000

Minor Renovation (a₂)$1,500$17,000$21,000

Probability0.250.530.22

a. Use the EMV criterion; should the owner expand or undertake minor renovations?(2 marks)

b-The owner has hired the services of an economist to forecast the change in the town's population, and she forecasts a slight increase in population. The accuracy of her predictions are as follows:

P(FD \ D)=0.75P(FD \ SI)=0.13P(FD \ I)= 0.12

P(FSI \ D) =0.15P(FSI \ SI) =0.65P(FSI \ I) = 0.23

P(FI \ D)=0.10P(FI \ SI)=0.22P(FI \ I)=0.65

FD = forecast decreaseFSI = forecast slightincreaseFI = forecast significant increase

Calculate the revised probability for each state of nature (to 3 decimal places)4 marks