Question

If a student attends every management science class, the probability of passing the course is 0.80; but if the student only attends randomly, then the probability of passing the course is 0.50. If a student fails, they can take a makeup test where the probability of passing is 0.60 if the student has attended every class. This probability of passing the makeup test drops to 0.10 if the student has attended at random. Passing the course is worth 5 credits. Full time attendance "costs" 3 credits in terms of energy and time whereas random attendance "costs" only 1 credit.Use a decision tree to decide which is the best attendance pattern to adopt.

Answer 1

Answer:

EV of node 4 = 0.6×5 + 0.4×0 = 3

EV of node 5 = 0.1×5 + 0.9×0 = 0.5

EV of node 2 = (0.8×5 + 0.2×EV of node 4) - 3

EV of node 2 = (0.8×5 + 0.2×3 ) - 3

EV of node 2 = 4.6 - 3

EV of node 2 = 1.6

EV of node 3 = (0.5×5 + 0.5×EV of node 5) - 1

EV of node 3 = (0.5×5 + 0.5×0.5 ) - 1

EV of node 3 = 2.75 - 1

EV of node 3 = 1.75

EV of node 3 is higher, therefore, best attend pattern is to attend randomly.