Recently, I learned how to solve the Monty hall Problem through Bayes' theorem. Since this is a direct way of proof, I was interested whether the problem can be solved by mathematical induction. However, I couldn't reach a conclusion, and I want to know two things:
1) Is it impossible to prove the Monty Hall problem through mathematical induction?
2) If then, why?
(My Maths is not that good so please explain it in an easy way!)