Management Science

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Management Science Quiz - Baye¡¦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 don¡¦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 ¡§drinkable¡¨ choices (hated a wine she liked) only 8% of the time, while you have agreed with her ¡§drinkable¡¨ 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.

SjP(Sj)P(I1|Sj)P(I1„xSj)P(Sj|I1)

Drinkable
90%87%.783.999
Dumpable
10%8%.008.010

.791
SjP(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____

What is the probability of the wine being acceptable if the wine critic says ¡§dumpable?¡¨ _.560___

What is the probability of the wine being unacceptable if the wine critic says ¡§drinkable?¡¨ _.010___

What is the probability of the wine being unacceptable if the wine critic says ¡§dumpable?¡¨ .440____

What is the probability of the wine being acceptable if the wine critic says ¡§drinkable?¡¨ _.999___
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