Q&A: The Monty Hall Problem
Originally published:
This is an English translation (via GPT-5.4). Read the original Hebrew version.
The Monty Hall Problem
Question
I didn’t understand why, in the three-door puzzle, there is a 66 percent chance that if you switch your choice, it will be correct. After all, once the host opens the door and there’s a goat there, we go back to square one, and then the chance is 50 percent. Right?
Answer
Discussion on Answer
Indeed, just a simple mistake. One-half and one-third do not add up to 1.
You wrote in the column that by switching, the chances of winning are half. In fact, the chances are two-thirds. Switching your choice after the host reveals one of the two remaining envelopes is equivalent to choosing the two remaining envelopes together (two envelopes out of three = 2/3).