In the past, when there was low demand, Professor Leung's predictions were favourable 11% of the time. The professor's predictions have also been unfavourable given high demand 28% of the time, and favourable given medium demand 60% of the time. Assume prior probabilities of 0.2 and 0.5 for low and medium 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 represents P(Low | Favourable) The last cell of the table represents P(High | Unfavourable) Low Medium Favourable 40.149 60 Unfavourable .6 x High b. Determine the marginal probabilities of favourable and unfavourable predictions. P(Favourable) = P(Unfavourable) =