probability problem decision theory
I have a decision theory problem:
There are 2 courses available to take in a department. The probabilities to get scores A, B or C are :
Course P(A) P(B) P(C)
X 0.1 0.7 0.2
Y 0.3 0.4 0.3
Where the next values has to be achieved:
A: 4 points
B: 3 points
C: 2 points
To gradute you need at least a B
To get and award you need at most A, but not C
Your choices are : take X, Y or both
What is the optimal decision if you want to graduate?
What is the optimal strategy if you want to get an award?
complete problem taking courses
Here is the complete problem statement:
There are two classes that you are thinking to take next semester: X and Y. Based on historical records, the possible probabilitie to obtain the grades A, B or C for the classes are:
for class X:
P(A) = 0.1
P(B) = 0.7
P(C) = 0.2
for class Y:
P(A) = 0.3
P(B) = 0.4
P(C) = 0.3
In computing grades: A=4 points, B= 3 points, C=2 points.
To graduate you need at least a B average (3 points) among the courses you take next. You need at least an A, but not C to get an award.
Your choices are to take X, or Y, or both courses.
What is your optimal decision to maximize your probability to graduate?
What is your optimal decision to maximize your probability to get an award?