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 36% of the time. The professor's predictions have also been unfavourable given high demand 37% of the time, and favourable given low demand 28% of the time.

Assume prior probabilities of 0.5 and 0.2 for low and high demand respectively.

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 represents P(Low | Favourable) The last cell of the table represents P(High | Unfavourable)

	Low	Medium	High
Favourable
Unfavourable

Determine the marginal probabilities of favourable and unfavourable predictions.

P(Favourable) =

P(Unfavourable) =