Before making a final decision on the production plan to adopt, the bakery's manager decides to contact Professor Leung in the Math Department to conduct a market research survey. The results of the survey will indicate either favourable or unfavourable market conditions for premium breads. In the past, when there was medium demand, Professor Leung's predictions were favourable 43% of the time. The professor's predictions have also been unfavourable given low demand 90% of the time, and favourable given high demand 77% of the time. Assume prior probabilities of 0.2 and 0.3 for medium and low demand respectively.

a.) Calculate posterior (revised) probabilities and enter them in the table below. Round answers to 3 decimal places; do not round intermediate results. Note: The first cell of the table representsP(Low | Favourable) The last cell of the table representsP(High | Unfavourable)

	Low	Medium	High
Favourable
Unfavourable

b.) Determine the marginal probabilities of favourable and unfavourable predictions. P(Favourable)=P(Favourable)= P(Unfavourable)=P(Unfavourable)=