a) Complete the missing information in the given decision tree.

X:

Y:

Z:

p1:0.5, p2:? , p3:? , p4:?

L1:2 L2:50 L3:20 L4: ? L5: ? L6:? L7:?

b)

Solve the tree to find the values below (You can use SilverDecisions).

Expected value without perfect information (EVwoPI) =

Expected value with perfect information (EVwPI) =

Expected value of perfect information (EVPI)

Jane wants to get protected as much as possible against a possibly lethal virus but she is worried about developing a bad reaction to the current and only vaccine offered. If she gets vaccinated she may develop a bad reaction. The level of protection may vary depending on her reaction to the vaccine. If she does not get vaccinated, then her protection level will not be very high. Jane can get an allergy test before deciding on the vaccine. The following decision tree is developed to find the expected value of perfect information. Notice that this tree contains both the original decision tree and the reversed (sub)tree. Some of the parameter values are given. L1, L2,...,L7 are protection levels. Notes: Give numerical answers in decimal format (with TWO digits after the decimal) if they are not integer, otherwise write integer values. Point weights of boxes: Any box in part (a) : Any box in part (b) = 1:3 Bad reaction L1 Get vaccinated p1 No bad reaction L2 p2 Don't get vaccinated L3 Y A L4 p3 Don't get vaccinated L5 Get allergy test Get vaccinated L6 No bad reaction p4 N L7 Jane wants to get protected as much as possible against a possibly lethal virus but she is worried about developing a bad reaction to the current and only vaccine offered. If she gets vaccinated she may develop a bad reaction. The level of protection may vary depending on her reaction to the vaccine. If she does not get vaccinated, then her protection level will not be very high. Jane can get an allergy test before deciding on the vaccine. The following decision tree is developed to find the expected value of perfect information. Notice that this tree contains both the original decision tree and the reversed (sub)tree. Some of the parameter values are given. L1, L2,...,L7 are protection levels. Notes: Give numerical answers in decimal format (with TWO digits after the decimal) if they are not integer, otherwise write integer values. Point weights of boxes: Any box in part (a) : Any box in part (b) = 1:3 Bad reaction L1 Get vaccinated p1 No bad reaction L2 p2 Don't get vaccinated L3 Y A L4 p3 Don't get vaccinated L5 Get allergy test Get vaccinated L6 No bad reaction p4 N L7