The tables below show prior, conditional, joint, marginal, and posterior probabilities for 3 states of nature: Good, Fair, and Poor. Encouraging and Discouraging are the possible forecasts of sample information. Encouraging Prior Conditional Joint Posterior Good 0.25 0.3 0.075 0.205 Fair 0.35 0.44 0.154 0.422 Poor 0.4 0.34 0.136 0.373 Discouraging Prior Conditional Joint Posterior Good 0.25 0.175 0.276 Fair 0.35 0.56 0.196 0.309 Poor 0.4 0.66 0.264 0.416 Use the given tables to determine the following probabilities: a) P(Fair) = b) P(Encouraging | Good) = c) P(Discouraging | Fair) = d) P(Discouraging and Poor) = e) P(Encouraging and Good) = f) P(Fair | Discouraging) = g) P(Good | Encouraging) = h) P(Discouraging) = Next