Management Science

Management Science Quiz - BayeÐŽ¦s Rule

You have invited your boss to come to your house for dinner and you want to select a good wine. To create a good impression, you are considering serving a new wine you recently found. Unfortunately, you could find only one bottle, and you donÐŽ¦t want to open it. Based on other wines from the same vineyard, you estimate there is only a 10% chance the wine will be unacceptable (acceptable being the only other state-of-nature). A noted wine critic has offered her opinion of the vintage in question (she rates wines as either drinkable or dumpable). In the past, you have disagreed with her ÐŽ§drinkableЎЁ choices (hated a wine she liked) only 8% of the time, while you have agreed with her ÐŽ§drinkableЎЁ choices 87% of the time. Use the table to calculate the final probabilities of the wine being acceptable if you choose to consult the wine critic, and then answer the specific questions shown below. Show all calculations to three decimal places.

Sj P(Sj) P(I1|Sj) P(I1„xSj) P(Sj|I1)

Drinkable

90% 87% .783 .999

Dumpable

10% 8% .008 .010

.791

Sj P(Sj) P(I2|Sj) P(I2„xSj) P(Sj|I2)

Drinkable

90% 13% .117 .560

Dumpable

10% 92% .092 .440

.209

What is the initial probability the wine is acceptable? _.791____

What is the initial probability the wine is unacceptable? _.209____