Average: /4 Attempts: Aa Aa E 5. Probabilities using a tree diagram A recent stu

Question

Average: /4 Attempts: Aa Aa E 5. Probabilities using a tree diagram A recent study in the Journal of Consumer Research suggests that appetite stimuli can make people more impatient in unrelated areas. [Source: Li, X. (2008). The effects of appetitive stimuli on out-of-domain consumption impatience. Journal of Consumer Research, 34. Participants in the study, all college students, were asked to serve as photo editors for a magazine. Half were randomly selected to view appetite-stimulating pictures of desserts, and the other half viewed non-appetite- stimulating nature pictures. Then the participants were offered a choice between a lottery ticket with a small, fast payout and a lottery ticket with a large, deferred payout. The lottery ticket with a small, fast payout is the impatient option, since it's associated with more immediate (less delayed) benefits than the lottery ticket with the large, deferred payout. A total of 61% of the students who viewed dessert photographs picked the lottery ticket with a small, fast payout, while 42% of the students who viewed nature photographs chose this option. Consider this statistical experiment: The study is rerun on a randomly selected college student Let D the event the student views dessert pictures, the event the student views nature pictures, the event the student picks the lottery ticket with a small, fast payout, and the event the student picks the lottery ticket with the large, deferred payout. The following tree diagram depicts the process of the student being randomly assigned to view either dessert or nature pictures (Step 1) and his or her subsequent choice between the lottery ticket with a small, fast payout and the lottery ticket with the large, deferred payout (Step 2).

Explanation / Answer

Probability #1 = 0.5

(half ofthe students were selected to view picture of desserts)

Probability #2 = 1-0.61 = 0.39

(61% chose lottery with fastn small payout, which means the remaining 39% chose the lottery with large, deffered payout)

Probability #3 = 0.5x (1-0.42)

= 0.5x 0.58 = 0.29

P(large, deferred payout) = 0.5x0.39 + 0.5x0.58 = 0.485

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