The government of Wano country is deciding between allowing or denying entry to tourists to the country due to an ongoing pandemic in the rest of the world. Wano country relies heavily on tourism for employment and denying tourists from entering will have a terrible impact on its economy. Currently none of its citizens have been infected by the disease causing the pandemic. Tourism to the country has already been affected due to the pandemic. If Wano country allows a person to enter, the government estimates the revenue gained per person they let enter the country to be $800. However, there is a 2% chance that a person is a carrier of the disease. In that case, the government estimates the total cost to deal with an infected person and related repercussions to be $5656 (note that this already factors in the revenue gained by allowing the person to enter). If Wano country denies a person from entering, the government estimates the cost to the economy to be $2000 per person that is refused entry. The government of Wano country is deciding between two types of tests to help in screening tourists. The first test is the PCR test, with both sensitivity and specificity being 0.99. The second test is an ART test. If a person is not infected, the ART test would be negative with probability 0.97. If a person is infected, the ART test would be positive with probability 0.8. Draw the decision tree for this decision problem faced by the government of Wano country, considering all decisions. You may assume the decision is made on a per person basis. Please answer the following questions. For your decision tree, what is the maximum expected revenue gained per tourist? Please round to 1 decimal place. The government of Wano country is deciding between allowing or denying entry to tourists to the country due to an ongoing pandemic in the rest of the world. Wano country relies heavily on tourism for employment and denying tourists from entering will have a terrible impact on its economy. Currently none of its citizens have been infected by the disease causing the pandemic. Tourism to the country has already been affected due to the pandemic. If Wano country allows a person to enter, the government estimates the revenue gained per person they let enter the country to be $800. However, there is a 2% chance that a person is a carrier of the disease. In that case, the government estimates the total cost to deal with an infected person and related repercussions to be $5656 (note that this already factors in the revenue gained by allowing the person to enter). If Wano country denies a person from entering, the government estimates the cost to the economy to be $2000 per person that is refused entry. The government of Wano country is deciding between two types of tests to help in screening tourists. The first test is the PCR test, with both sensitivity and specificity being 0.99. The second test is an ART test. If a person is not infected, the ART test would be negative with probability 0.97. If a person is infected, the ART test would be positive with probability 0.8. Draw the decision tree for this decision problem faced by the government of Wano country, considering all decisions. You may assume the decision is made on a per person basis. Please answer the following questions. For your decision tree, what is the maximum expected revenue gained per tourist? Please round to 1 decimal place
