PLEASE SHOW WORK 9. The Three Prisonrs An unknown two will be shot, the other fr

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PLEASE SHOW WORK

9. The Three Prisonrs An unknown two will be shot, the other freed. Prisoner A asks the warder for the name of one other than himself who will be shot, explaining that as there must be at least one, the warder won't really be giving anything away. The warder agrees, and says that B will be shot. This cheers A up a little: his judgmental probability for being shot is now 1/2 instead of 2/3 Show (via Bayes theorem) that a) A is mistaken- assuming that he thinks the warder is as likely to say "C as "B" when he can honestly say either; but that (b) A would be er will say "R" whenever he honestly can. right, on the hypothesis th the war

Explanation / Answer

a) If the warden is likely to say C or B when he can, means that he is agnostic between B and C

The three options are

AB

AC

BC

P(A/B)=P(A intersection B)/P(B) = 2/3*2/3 /[2/3]=2/3

b) If the warden will say B whenever he can say honestly, the two options are AB and BC.

P( A being shot) = 1/2 in this case

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