Management Science Quiz – Baye*ƒ*…½*ƒ‚¦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*ƒ*…½*ƒ‚¦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 *ƒ*…
½*ƒ‚§drinkable*ƒ*…½*ƒ choices (hated a wine she liked) only 8% of the time, while you
have agreed with her *ƒ*…½*ƒ‚§drinkable*ƒ*…½*ƒ 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*…¾xSj) P(Sj|I1)
Drinkable
90% 87% .783 .999
Dumpable
10% 8% .008 .010
.791
Sj P(Sj) P(I2|Sj) P(I2*…¾xSj) 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 *ƒ*…
½*ƒ‚§dumpable?*ƒ*…½*ƒ _.560___
What is the probability of the wine being unacceptable if the wine critic says *ƒ*…
½*ƒ‚§drinkable?*ƒ*…½*ƒ _.010___