Maximizing the expected profits: Consider W is the event that represents the weather is warm and C is the event that represent the weather is cold. Also, assume that C p is the event that represents the expert predicts the weather is cold and W p is the event that represents the expert predicts the weather is warm. States of nature Strategies Warm (W) Cold (C) Wheat 7000 6500 Corn 8000 5000 Probability 0.6 0.4 There is 90% of chance that the expert predicts year is cold and it is actually cold, i.e., conditional probability which is given as follows: P(C p |C) = 0.90 Therefore, the probability that the weather is predicted as warm when it was cold is given as follows: P(W p |C) = 1 - P(C p |C) = 1 – 0.9 = 0.10 Similarly, it is given that 80% of times the weather is actually warm and the expert also predicted the same, i.e., P(W p |W) = 0.80 Also, P(C p |W) = 0.20 Calculate the probability that an expert predicts correctly or incorrectly. Let, CP and ICP denote the events correct prediction and incorrect prediction by expert. Therefore, the probabilities are as follows: P(CP) = P(W p |W) x P(W) + P(C p |C) x P(C) = (0.80 x 0.60) + (0.9 x 0.40) = 0.48 + 0.36 = 0.84 P(CP) = P(C p |W) x P(W) + P(W p |C) x P(C) = (0...

Question

In a party, there are 10people with white shirts and 8 people with red shirts; 4 people have black shoes and white shirts; 3 people have black shoes and red shirts; The total number of people with white or red shirts or black shoes is 21. How many people have black shoes?

Answer 1

Expert Solution & Answer

Chapter 13.5, Problem 3P

Explanation of Solution

Maximizing the expected profits:

Consider W is the event that represents the weather is warm and C is the event that represent the weather is cold.

Also, assume that C_p is the event that represents the expert predicts the weather is cold and W_p is the event that represents the expert predicts the weather is warm.

States of nature
Strategies Warm (W) Cold (C)
Wheat 7000 6500
Corn 8000 5000
Probability 0.6 0.4

There is 90% of chance that the expert predicts year is cold and it is actually cold, i.e., conditional probability which is given as follows:

P(C_p|C) = 0.90

Therefore, the probability that the weather is predicted as warm when it was cold is given as follows:

P(W_p|C) = 1 - P(C_p|C)

              = 1 – 0.9

              = 0.10

Similarly, it is given that 80% of times the weather is actually warm and the expert also predicted the same, i.e.,

P(W_p|W) = 0.80

Also, P(C_p|W) = 0.20

Calculate the probability that an expert predicts correctly or incorrectly. Let, CP and ICP denote the events correct prediction and incorrect prediction by expert. Therefore, the probabilities are as follows:

P(CP) = P(W_p|W) x P(W) + P(C_p|C) x P(C)

           = (0.80 x 0.60) + (0.9 x 0.40)

           = 0.48 + 0.36

           = 0.84

P(CP) = P(C_p|W) x P(W) + P(W_p|C) x P(C)

           = (0...

Explanation of Solution

Calculating EVSI:

Expected Value of Sample Information (EVSI) is referred to as the value of information that would be obtained from sample information. For this, first determine the expected value with the sample information (EVWSI). This is the sum of the expected value when weather forecast is performed plus the cost of weather forecast.

EVWSI = (Expected value) + (Cost of hiring expert)

              = 6259.4 + 600

              = 6859.4

The EVWOI value is 6800. Therefore,

EVSI = EVWSI – EVWOI

          = 6859.4 – 6800

          = $59...

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