5. (Entropy as an amount of uncertainty; the King's poisoned wine.) Joffrey Baratheon has 1000 barrels...

 

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5. (Entropy as an amount of uncertainty; the King's poisoned wine.) Joffrey Baratheon¹ has 1000 barrels of excellent wine that he wishes to serve at the annual feast in one week, but an informant warns him that one of them is poisoned: any person who drinks even a drop of the wine will die 5 days later. Since Joffrey is the worst, he decides to force his prisoners to test the wine for him. If he had 1000 prisoners, this would be simple; however, he has only 10. (a) Explain why it is possible for Joffrey to solve his problem in time for the feast by calculating the entropy of the random variable W which represents the identity of the poisoned barrel and interpreting the meaning of this quantity. (b) (Bonus) Find a strategy that will allow Joffrey to determine which barrel holds the poisoned wine. 5. (Entropy as an amount of uncertainty; the King's poisoned wine.) Joffrey Baratheon¹ has 1000 barrels of excellent wine that he wishes to serve at the annual feast in one week, but an informant warns him that one of them is poisoned: any person who drinks even a drop of the wine will die 5 days later. Since Joffrey is the worst, he decides to force his prisoners to test the wine for him. If he had 1000 prisoners, this would be simple; however, he has only 10. (a) Explain why it is possible for Joffrey to solve his problem in time for the feast by calculating the entropy of the random variable W which represents the identity of the poisoned barrel and interpreting the meaning of this quantity. (b) (Bonus) Find a strategy that will allow Joffrey to determine which barrel holds the poisoned wine.

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5 a The entropy of a random variable measures the amount of uncertainty associated with it In this case W represents the identity of the poisoned barr... View the full answer