Thread: 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?

thanks

Originally Posted by rbenito

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

The next bit does not seem to have any use in this question:

Where the next values has to be achieved:
A: 4 points
B: 3 points
C: 2 points

The available decisions are: take X only, take Y only, take both.
As far as I can see decision 3 dominates the others, so irrespective
of what the precise numbers are the optimal strategy is to take both.

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?

thanks

RonL

Remember the courses are X and Y, the choices are: take X, take Y or take both. The letters A,B or C are related to the scores.
what is the optimal strategy?

Originally Posted by rbenito

Remember the courses are X and Y, the choices are: take X, take Y or take both. The letters A,B or C are related to the scores.
what is the optimal strategy?

It makes no difference how the courses are labelled taking both dominates
taking only one, so there is no calculation to be done.

RonL

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?

thanks