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 0.1 0.34 0.034 0.055 Fair 0.4 0.5 0.2 0.326 Poor 0.5 0.76 0.38 0.619 Discouraging Prior Conditional Joint Posterior Good 0.1 0.66 0.066 0.171 Fair 0.4 0.5 0.2 0.518 Poor 0.5 0.24 0.12 0.311 Use the given tables to determine the following probabilities: a) P(Fair) = b) P(Encouraging | Poor) = c) P(Discouraging | Poor) = d) P(Discouraging and Fair) = e) P(Encouraging and Good) = P(Poor | Discouraging) = 9) P(Good | Encouraging) = h) P(Discouraging) Next