Problem #PRU-66046

Problems Probability and statistics Probability theory Discrete distribution Set theory and logic Theory of algotithms Theory of algorithms (other)

Problem

In one box, there are two pies with mushrooms, in another box there are two with cherries and in the third one, there is one with mushrooms and one with cherries. The pies look and weigh the same, so it’s not known what is in each one. The grandson needs to take one pie to school. The grandmother wants to give him a pie with cherries, but she is confused herself and can only determine the filling by breaking the pie, but the grandson does not want a broken pie, he wants a whole one.

a) Show that the grandmother can act so that the probability of giving the grandson a whole pie with cherries will be equal to \(2/3\).

b) Is there a strategy in which the probability of giving the grandson a whole pie with cherries is higher than \(2/3\)?