Problem 2 (20 pts) A subset of King Robert I\'s small council has assembled, per

Question

Problem 2 (20 pts) A subset of King Robert I's small council has assembled, per instructions from their king, for a secret conclave. In attendance are: Jon Arryn Hand of the King Pycelle Grand Maester Petyr Baelish Master of Coin Renly Baratheon Master of Laws Stannis Baratheon Master of Ships Barristan Selmy Lord Commander of the Kingsquard The six members enter a room and take seats around a round table. Before their meeting, however, Varys (Master of Whisperers) mounted a tiny device that can shoot a poisoned dart underneath the table at one of the six seats. He was not entirely sure where each individual would sit at this conclave, but his network of spies has gathered a great deal of information about the habits and motives of all the attendees, and with that information Varys has come up with the following calculations:

Explanation / Answer

we need to find the prob(Dart mounted at Renly's Seat | Jon Arryn was poisoned)

=P(Dart Mounted at Renly's Seat & Jon Arryn was Poisoned)/P(jon Arryn was poisoned)

P(Dart Mounted at Renly's Seat & Jon Arryn was Poisoned)=0.44*0.34*0.16=0.023936

P(Dart Mounted at Petyr's Seat & Jon Arryn was Poisoned)=0.42*0.99*0.2=0.08316

P(Dart Mounted at Pycelle's Seat & Jon Arryn was Poisoned)=0.14*0.86*0.1=0.01204

P(jon Arryn was poisoned)=0.44*0.34*0.16+0.42*0.99*0.2+0.14*0.86*0.1=0.119136

hence prob=0.023936/0.119136=44/219=0.2009

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