Response to each post:
This is a great discussion question! I conceptually understood the reason for switching doors after the initial explanation, but my â€œgutâ€ kept saying stick with what you picked because now you have a 50/50 chance of having the right door. This is incorrect though, I still only have a 1/3 chance of having picked the correct door. The 1 out of 100 doors shows this more clearly, as the presenter stated, because 1/100 makes more since of having less of a chance than 1/3.
The trick (on the part of the game) was making people thing they had a 50/50 chance of picking the car (A) because a goat had already appeared (B) behind another door. That would only be accurate if they had opened the door revealing B and then let you pick where you though (A) was; then you would truly be making a choice out of two options. But it doesnâ€™t work that way, you still only had a 1 in 3 chance of picking correctly (A), they showed a goat (B) behind another door, but you still only had a 1 in 3 chance of picking A, which is less than the 2 out of 3 chances it was another door.
Iâ€™ve done a horrible job of explaining it, but look at it from the games point of view, if you didnâ€™t have less of a chance of making the correct choice initially, and then sticking with you original choice because you thought your chances went to 50/50, the show would have given out a lot more cars which wasnâ€™t the goal of the show.
I learned a lot after watching the video about probabilities when you take the time to review what are the chances to get something. I also learned more about P(A)(B) is the formula to calculate the chances of me getting something based on what is dealt to me like on this cases it was doors.
It seems that switching the doors itâ€™s the best course of action because our chances will increase. However I disagree because I think you should stick with the one you selected initially since the game host on this case goal is to make sure you donâ€™t win and actually doubt your decision.