Monty Hall problem
1. Suppose we play modified version of Monty Hall game. In this version, there're five doors instead instead three. Four of the doors have goats, and one haves the car. As before, you choose a door, but before opening it you've the opportunity to switch. This time, however, Monty opens two of the remaining four doors and shows that they contain goats (he chooses amongst the doors containing goats randomly). After this, you are given the choice to either stay with your chosen door, or to switch to one of the other closed doors. If you switch, what is the probability that you will get the car? Show your work