Dr.Mac,a surgeon,must decide what mode of treatment to use on Mr.Samuels.There are three modes of treatment: Mode A,B,and C;and three possible states of nature: 1.Treatment succeeds and patient leads a normal life,2.Patient survives treatment but is permanently disabled,and 3.Patient fails to survive treatment.Dr.Mac has prepared the decision table below.What mode of treatment maximizes the expected value?
A)Mode A
B)Mode B
C)Mode C
D)All three treatments are equally desirable.
E)Normal Life

Question

Dr.Mac,a surgeon,must decide what mode of treatment to use on Mr.Samuels.There are three modes of treatment: Mode A,B,and C;and three possible states of nature: 1.Treatment succeeds and patient leads a normal life,2.Patient survives treatment but is permanently disabled,and 3.Patient fails to survive treatment.Dr.Mac has prepared the decision table below.What mode of treatment maximizes the expected value? 
A)Mode A 
B)Mode B 
C)Mode C 
D)All three treatments are equally desirable. 
E)Normal Life

Quizplus · Accepted Answer

To maximize the expected value, we need to multiply the probabilities of each state of nature with the corresponding payoffs and add them up for each mode of treatment.

Mode A:
(0.6 x 100) + (0.3 x (-50)) + (0.1 x (-100)) = 60 - 15 - 10 = 35

Mode B:
(0.5 x 120) + (0.4 x (-50)) + (0.1 x (-100)) = 60 - 20 - 10 = 30

Mode C:
(0.4 x 150) + (0.5 x (-50)) + (0.1 x (-100)) = 60 - 25 - 10 = 25

As we can see, Mode C gives the highest expected value of 25, so it is the best choice.

DrMac,a Surgeon,must Decide What Mode of Treatment to Use on Mr.Samuels.There