Aa Aa E. 10. Probabilities using a tree diagram, Bayes\' theorem A recent study

Question

Aa Aa E. 10. Probabilities using a tree diagram, Bayes' theorem A recent study in the Journal of Consumer Research suggests that appetite stimuli can make people more impatient in unrelated areas. 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 larger, deferred payout. The lottery ticket with a small, fast payout is the impatient option because it's associated with more immediate (less delayed) benefits than the lottery ticket with the larger, deferred payout. [Source: Li, X. (2008). The effects of appetitive stimuli on out-of-domain consumption impatience. Journal of Consumer Research, 34.] 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 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 sma fast payout, and the event the student picks the lottery ticket with the larger, 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 larger, deferred payout (Step 2).

Explanation / Answer

from above as half view dessert ; hence probabilty #1=0.5

probability #2 =1-0.61=0.39

probabilty #3 =0.5*(1-0.42)=0.29

1)probabilty of larger,deffered payout=0.5*0.39+0.5*0.58=0.485

2)probabilty of dessert picture =0.5

3)smaller

4)posterior probability =0.5*0.39/0.485=0.40

5) posterior probabilty =0.5*0.58/0.485=0.60

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