3 guys are on death row Only one will be not executed tomorr

3 guys are on death row. Only one will be not executed tomorrow morning. The guard told that Pete (among two others) one of the other men will be executed. Before Pete got the answer his probability was 1/3, after Pete got the answer, he is happy: probability 1/2 should he is happy? what’s wrong?

Solution

Consider the three guys to be P (Pete) , A and B

Thus,

P ( Choosing a pair to be executed) = (AB, PB, PA)

So, P (pete will not be executed) = 1/3 (i.e when AB is chosen)

Now,

Let\'s assume Pete\' knows B is the person that will definitely be executed.

Thus,

The choice now becomes = (PB or AB)

Thus, P ( He will be saved) = 1/2 i.e when AB is chosen.

Since, the probability of him being saved is increased, he must be happy.

Hope this clears your doubts.