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

Question

10. Probabilities using a tree diagram, Bayes' theorem Aa Aa 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 movie ticket and a bookstore coupon. The movie ticket is the impatient option because it's associated with more immediate (less delayed) benefits than the bookstore coupon. [Source: Li, X. (2008). The effects of appetitive stimuli on out-of-domain consumption impatience. Journal of Consumer Research, 34. A total of 70% of the students who viewed dessert photographs pickedte movie ticket, while 45% 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; N the event the student views nature pictures; M the event the student picks the movie ticket; and 8 the event the student picks the bookstore coupon. 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 movie ticket and the bookstore coupon (Step Step Step 2 (D, M) Probably #l Probabdity#2 (D. B) N, M) 04. B) Probabity#3 Find the vaiues of the three designated probabilities, and enter them in the following table (round probabilities to two decimal places). Probability Value

Explanation / Answer

from above :

1)

2)

P(bookstore option) =P(dessert and bookstore)+P(nature and bookstore)=0.5*0.3+0.5*0.55=0.425

3)

P(prior probability of nature)=0.5

4)

Bigger

5)posterior probability=0.5*0.55/0.425=0.6471~ 0.65

6)

posterior probability of dessert pics =1-0.65 =0.35

probability value probability #1 0.5 probability #2 0.3 probability #3 0.275

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