Question

.las.er Office Tab e Cceuns Pacci PeueHTUupceae Стили 11рифт 17 Tasks for students [ Режим orp 12 bring 60% ofthe positive result, and 40%-negative. Draw a Decision Tree showing these choices and choose the best choice 3. Using the decision shown (without probability), caleulate which option shoule selected on purely financial grounds. Show all your calculations to support your answe $50,000 Apartment buildin $30,000 $100,000 Office building -HO,000 Positivee report $30,000 $10.000 Apartment building $30,000 $100,000 Office building $40.000 $30.000 4. Try to determine the appropriate probabilities

Answer 1

This is a decision tree and we need to find the expected values at each node to finalize a path/option. The node with max expected values should be taken (purely on financial grounds).

Now, lets see how to calculate expected value. Consider following exampl

Node 2 $200 2 0.5 Node 1 . > Node 3 p = 0.5 - $100

Here, p represents the probability of the outcome. From Node 1 we can go to node 2 or node 3 and both have probabilities of 0.5.

Expected value of node 1, EMV (node 1) = [ probability (node 2) * value of node 2 ] + [ probability (node 3) * value of node 3 ]

                                                                 = [ 0.5 * 200 ] + [ 0.5 * (-100) ] = 100 - 50 = $50

Coming back to the question, probability is not given. We can also choose probabilities as 0.6 for success and 04 for failure, which is seen in top most line of image of the question.

Now, using above logic we can calculate expected value of nodes 4,5,6,7,8,9 in the question as follows.

Please note that

EMV (node 4) = EMV (node 7), EMV (node 5) = EMV (node 8) and EMV (node 6) = EMV (node 9), because outcomes are same and hence considering same probability will give same result.

EMV (node 4 or node 7) = (0.6 * 50000) + ( 0.4 * 30000) = $ 42,000

EMV (node 5 or node 8) = (0.6 * 100000) + ( 0.4 * (-40000)) = $ 44,000

EMV (node 6 or node 9) = (0.6 * 30000) + ( 0.4 * 10000) = $ 22,000

Now max of these 3 gives us: $44,000

From this result we can see that option 2 (Office building) is the way to go.

If we consider probility as 0.5 of each node, then

EMV (node 4 or node 7) = (0.5 * 50000) + ( 0.5 * 30000) = $ 40,000

EMV (node 5 or node 8) = (0.5 * 100000) + ( 0.5 * (-40000)) = $ 30,000

EMV (node 6 or node 9) = (0.5 * 30000) + ( 0.5 * 10000) = $ 20,000

In this case max = $40,000 which is option 1 (Appartment building)