Exercise 2.5 - The Monty Hall problem(The dilemma of three doors)

The answer is (b). Use ${\text{prize}}_i\text{, }{\text{choose}}_i\text{, }{\text{open}}_i$ to denote the event that the prize is in/the player chooses/the host opens the $i$-th box. Apply Bayes’s rules:

In the last step, we summarize the potential location of the prize. This is a classical example of anti-intuition results from probability.