DareDevil, is a reality television game show where contestants participate in three different

survival events: Ring of Fire, Alligator Swim, and Ultimate Bug Cave. All contestants can

choose in which sequence they participate in the three events. However, should they not

"survive" an event, they are not permitted to participate in the subsequent event (i.e., they

are out of the competition). The different events have prize money associated with them (as

described below) for survival. Rihanna Malik is a talented athlete (former Olympian) who has

trained for this show. She wants to carefully choose in which sequence to compete in the

three events to maximize her expected winnings. The prize money for surviving the three

events are provided in the following table, along with the probability of Rihanna surviving

each event in the competition (she is an elite athlete hence her probabilities of success are

quite high):

Event Winnings if Successful Probability of Success

Ultimate Bug Event $17,000 0.80

Ring of Fire $20,000 0.85

Alligator Swim $25,000 0.75

a. Create a decision tree for this problem that could be used to determine the order in

which she should compete in these events to maximize her expected winnings by

playing DareDevil. Draw this tree by hand and include it along with your submission.

Do not put any numbers (probabilities, costs, etc.) on your drawing.

The tree should show the structure and logic of the decision process.

Distinguishing between decision and chance nodes, and naming the various

nodes and branches, is critical.

Create a tree that is as general as possible - do not eliminate certain branches

from consideration because of the specific values of the inputs as presented

in the case.

Recall that the key to success is determining what decision/event happens

first, and then building out the tree in sequential order.

b. Implement your tree from part a in Precision Tree. Include a copy of the spreadsheet and snapshots of the tree so I can learn how to do it. You may wish to

view it in landscape mode and scale to fit 1 page wide by 2 pages tall.

c. State the optimal decision strategy regarding the order in which she should compete

in the three events?

d. What is Rihanna's expected winnings by competing in the events in this sequence?