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 Cave 517000 0.80 Ring of Fire 520000 0.85 Alligator Swim 525000 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 Da reDevil. Draw this tree by hand and include it along with your submission. 0 Do not put any numbers (probabilities, costs, etc.) on your drawing. 0 The tree should show the structure and logic of the decision process. 0 Distinguishing between decision and chance nodes, and naming the various nodes and branches, is critical. 0 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. 0 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. Print the tree out and include it along with your submission. (If it is hard to read on a single page, you may wish to print 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