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Adele is going to visit her parents in Spain once her exams are over in June. She has been searching for affordable tickets for her visit. Assume that she just completed an online search for tickets and she found a ticket at $550. She is undecided whether she should purchase now or later. If she purchases later, the price of ticket may drop to $500 with probability 0.7 and the price of the ticket may increase to $650 with probability 0.3.
a) What should Adele do? Should she purchase now or later? Show your work.
The website Adele is using provides a tool that predicts the future state of the ticket, i.e., price drop or price increase. From her earlier experiences, Adele does not find the tool very reliable. She believes that the probability that the tool predicts price increase when in reality the price of the ticket actually increases is 0.6. She also believes that the probability that the tool predicts price increase when the price of ticket actually drops is 0.7.
b) What is the probability that the tool predicts price drop for the ticket?
c) Given the reliability issues with the tool, should Adele use the tool while making the purchase decision?
d) Assume that Adele decided to use the tool while making her purchase decision. The tool predicts that the price of the ticket will decrease. Should Adele buy the ticket now or purchase later?
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