Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (S_I) represent the levels of demand for the company products. S₁, S₂, and S₃ characterize high, medium, and low demand, with probabilities of .3, .6, and .1, respectively. The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand. 48 monthly sales reports are randomly selected. These monthly sales reports show 15 months with high demand, 28 months with medium demand, and 5 months with low demand. 12 of the 15 months with high demand had favorable weather conditions. 14 of the 28 months with medium demand had favorable weather conditions. Only 1 of the 5 months with low demand had favorable weather conditions. The estimated probabilities of poor weather conditions given different levels of demand are presented below.
P(Poor |High) = .2, P(Poor |Medium) = .5, P(Poor |Low) = .8
What is the probability of high demand given that the weather conditions are poor?

Question

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt. The level of demand affects the success of both strategies. The states of nature (S_I) represent the levels of demand for the company products. S₁, S₂, and S₃ characterize high, medium, and low demand, with probabilities of .3, .6, and .1, respectively. The payoff values are in thousands of dollars.

The management believes that weather conditions significantly affect the level of demand. 48 monthly sales reports are randomly selected. These monthly sales reports show 15 months with high demand, 28 months with medium demand, and 5 months with low demand. 12 of the 15 months with high demand had favorable weather conditions. 14 of the 28 months with medium demand had favorable weather conditions. Only 1 of the 5 months with low demand had favorable weather conditions. The estimated probabilities of poor weather conditions given different levels of demand are presented below.
P(Poor |High) = .2, P(Poor |Medium) = .5, P(Poor |Low) = .8
What is the probability of high demand given that the weather conditions are poor?

Quizplus · Accepted Answer

P(High│Poor) = P(High ∩ Poor)/P(Poor) = (P(High) × P(Poor│High))/P(Poor)
= (.3125 × .2)/(21/48) = .0625/.4375 = .1429

Alternatives 1 and 2 in the Following Payoff Table Represent