Please help!!!
3. A one-legged, red-nosed tramp approaches John in the park and tells him he can predict the next day’s weather perfectly after he has drunk a shot of “Ripple” wine (cost of one shot: $0.50). If the tramp is telling the truth, should John engage in this transaction?
a) Yes
b) No
c) Not enough information to answer this question.
4. Assume that John is using minimax regret criteria, how many dozen should he buy?
a) 0
b) 1
c) 1.5
d) 2
e) 2.5
5. If the weather bureau’s forecast for the next day is 30 percent chance of rain, 20 percent chance of being sunny, how many dozen bars should he buy for tomorrow?
a) 0
b) 1
c) 2
d) 3
6. The value of perfect information is:
a) 4
b) 20
c) 24
d) 45
e) 54
To answer these questions, let's break down each question and explain how to arrive at the answer.
3. The question asks if John should engage in the transaction with the tramp if the tramp is telling the truth about predicting the weather after drinking Ripple wine. However, we don't have enough information to accurately assess the situation. We would need more information about the tramp's past predictions and the accuracy of those predictions. Therefore, the answer is c) Not enough information to answer this question.
4. The question mentions that John is using minimax regret criteria to make a decision. Minimax regret is a decision-making strategy that minimizes the maximum possible regret. To determine the number of dozens John should buy, we need to calculate the regret for each possible choice. The options given are 0, 1, 1.5, 2, and 2.5 dozens. Calculate the regret for each choice by comparing it to the best possible outcome. The choice with the lowest maximum regret is the optimal choice according to minimax regret criteria. Once the regrets are calculated, choose the option with the lowest maximum regret. The answer depends on the specific data and calculations provided in the context of the problem.
5. In this question, we need to estimate how many dozen bars John should buy based on the weather forecast. The forecast indicates a 30% chance of rain and a 20% chance of being sunny. To make this decision, calculate the expected value for each choice by multiplying the probability of each outcome by the value associated with that outcome. In this case, the value is the number of dozen bars. The option with the highest expected value is the optimal choice. From the options given (0, 1, 2, 3), calculate the expected value for each choice and choose the option with the highest expected value.
6. The value of perfect information is the difference between the maximum expected value with perfect information and the maximum expected value without perfect information. Unfortunately, the context or information necessary to calculate the expected values is missing in the question. Without that information, it is not possible to determine the value of perfect information. Therefore, there is not enough information to answer this question.