Question
Only Part b.
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Q10. a) Three prisoners are informed by their jailer that one of them has been chosen at random to be executed, and the other two are to be freed. Prisoner A asks the jailer to tell him privately which one of the other prisoners will be freed, claiming that that there would be no harm in divulging this information, since he already knows that at least one of them will go free. The jailer refuses to answer this question, pointing out that if A knew which of his fellow prisoners were to be set free, then his own probability of being executed would rise from 1/3 to 1/2, since he would then be one of two prisoners. What do you think of the jailer's argument? b) A more positive way to pose a similar question is as follows. You are a game contestant. In the game, there are three boxes, two of which are empty and the third has $1M in it. You pick a box. The game show host now opens one of the other boxes and shows it to be empty. You now have the choice of staying with your original selection or switching to the other box. What should you do and why?
Explanation / Answer
Answer:(b)
number of boxes =3
probability of picking first box=1-(2/3)
=1/3
probaility of remaining two boxes =2/3
probablity of box which was open by host=1-(2/3) =1/3
If picking box is empty there is a chance to switch another box .Therefore theprobability of box is 1/3.
