Assignment:
In a game show, a contestant is given a choice of 3 curtains. Behind one curtain is a prize, but the other two curtains conceal a sign saying "Sorry, you lose!". After the contestant chooses a curtain, the host, who knows where the prize is, will always open one of the curtains (not the one chosen by the contestant) to reveal a worthless sign. The contestant then has the option to stick with their original choice or switch to the remaining closed curtain. Model this problem in detail with a probability space. What should the contestant do?
Provide complete and step by step solution for the question and show calculations and use formulas.