RE: Would you switch?
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This was also in the Da Vinci Code book, and the subsequent discussion resulted in many mathematicians getting it wrong.
The best way I've heard it explained is to increase the number of doors to a ridiculous level (like 100). But for the life of me I can't remember why this helps in understanding the problem. Perhaps someone else can work it out.
edit: Ok, I read down the comments and see someone else talked about this. Imagine 100 doors, with 99 having a penny and one having a million dollars. The assistant will open 98 doors with a penny behind, leaving you two doors and the option to swap. Probability suggests you should swap, as the odds of you initially picking the million dollar door is a terrible 1 in a 100. By swapping, you increase your odds to 50%.
This is the first explanation that makes sense to me! And even then, my head is still going in circles :D
Definitely more than 50%. Your first choice has a very high likelihood of being penny door, so the chances that the other door has 1M dollars after the reveal would also be very likely. (99%)
I like this way of explaining the problem though, it really can help with the intuition.
No with 100 doors you increase your odds of winning to 99%.
Since when you picked the door initially you had a 1% chance of being correct, now you have a lot of additional information.
It is not a 50% 50% due to the fact that the door you picked was 1% so the other door is 99%.
Yep, correct.