Question

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 an apartment with a great view and an apartment close to work. The apartment with a great view is the impatient option because it’s associated with more immediate (less delayed) benefits than the apartment close to work. [Source: Li, X. (2008). The effects of appetitive stimuli on out-of-domain consumption impatience. Journal of Consumer Research, 34.]

A total of 65% of the students who viewed dessert photographs picked the apartment with a great view, while 60% 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;
V	=	the event the student picks the apartment with a great view; and
W	=	the event the student picks the apartment close to work.

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 apartment with a great view and the apartment close to work (Step 2).

  

Find the values of the three designated probabilities, and enter them in the following table (round probabilities to two decimal places).

Probability	Value
Probability #1
Probability #2
Probability #3

What is the probability that the randomly selected student picks the apartment with a great view?

0.375

0.5

0.975

0.625

What is the prior probability that the randomly selected student viewed nature pictures?

0.6

0.8

0.3

0.5

Now use the information that the student picked the apartment with a great view to compute the posterior probability that the student viewed nature pictures. The posterior probability is   .

Given the information that the student picked the apartment with a great view, what’s the posterior probability that the student viewed dessert pictures?

0.33

0.30

1.92

0.52

Answer 1

Tree Diagram:

What is the probability that the randomly selected student picks the apartment with a great view?

= 0.65 (0.50) + 0.60 (0.50)

P(V)   =  0.625

What is the prior probability that the randomly selected student viewed nature pictures?

From the tree diagram, P(N) = 0.5

Using the information that, the student picked the apartment with a great view, to compute the posterior probability that the student viewed nature pictures. The posterior probability is   .

  

= 0.48

Given the information that the student picked the apartment with a great view, what’s the posterior probability that the student viewed dessert pictures?

  

= 0.52