question:

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 0.4 0.2 0.08 0.426 Fair 0.4 0.1 0.04 0.213 Poor 0.2 0.34 0.068 0.362 Discouraging Prior Conditional Joint Posterior Good 0.4 0.8 0.32 0.394 Fair 0.4 0.9 0.36 0.443 Poor 0.2 0.66 0.132 0.163 Use the given tables to determine the following probabilities: a) P(Poor) = b) P(Encouraging | Good) = c) P(Discouraging | Poor) = d) P(Discouraging and Fair) = e) P(Encouraging and Poor) = f) P(Poor | Discouraging) = g) P(Poor | Encouraging) = h) P(Encouraging) =