You have been invited to a game show Now is your chance to w

You have been invited to a game show. Now is your chance to win a car! The rules are as follows: There are 3 doors on stage. Behind 2 doors are goats, behind the 3rd one is the car. You choose a door. However, before opening your chosen door, the presenter opens a second door to reveal a goat and offers you the choice: will you switch doors (there are now two unopened doors: your initial choice and another one) or keep with your initial choice? Which option should you choose to maximize your chances of winning a car? Explain your reasoning clearly using what we have seen in class.

Solution

I will switch.

Initially, when I chose, I am more probably wrong, as I only have 1/3 chance to get it.

However, this time, he gives a given that one of the doors (something I could have chosen) to be a goat. Thus, the probability of choosing correctly this time will be better than choosing the last time.

Thus, SWITCHING DOORS is a better choice.