A firm is deciding between using one of 3 possible suppliers. They are unsure of which supplier will provide the best service;in the absence of any additional information, supplier 2 is twice as likely to be suitable as suppliers one and three. In other words, supplier 2 is the correct choice with probability .5, and each of the other two are the best choice with probability .25.

A data scientist claims that an algorithm can provide insight into supplier one by studying past deliveries by supplier 1. The data scientist claims (and we'll take all of these claims to be accurate) that if supplier 1 is the not the right choice (i.e. if the right choice is one of the suppliers 2 or 3), the analysis will surely uncover a complaint against supplier 1 (i.e. with probability 1). On the other hand, if supplier 1 is the right choice, it might still will find a complaint against it 1/2 the time, and not find one 1/2 of time. (Again take these probabilities to be correct.)

1. Suppose the algorithm comes back indicating no complaint against supplier 1. How likely is supplier 1 the best choice?

1. Suppose the algorithm comes back indicating a complaint against supplier 1. If the firm chooses a supplier that maximizes their chances of being right, how likely it the supplier they choose to be the right one?

1. Before knowing the outcome of the investigation, how likely is the firm to choose the right supplier, if follows the best choice from the cases described in (1) and (2)?

1. Suppose that choosing a correct supplier has a payoff of +18 million dollars, and a wrong supplier has a payoff of -6 million dollars. How much is the data analysis worth, in terms of improved EV for the firm? (The answer should be one number, from the standpoint of before the analyst's report is revealed.)

1. Note that both supplier 1 and 3 are equally likely to be suited to the firm, unconditionally. Are they equally likely to be chosen when the firm has access to the algorithm?