Why does the probability “lock in” and not change if you remove a variable but doubles for the other one?
I read it multiple times and it still doesnt make any logical sense to me.
In: Mathematics
Imagine:
1. You are a contestant on a game show, and there are three doors in front of you.
2. Behind one of the doors is a car (the prize you want), and behind the other two doors are goats.
3. You pick a door, let’s say Door #1.
4. The host, Monty Hall, who knows what’s behind each door, opens another door (let’s say Door #3) revealing a goat.
5. Now, there are two doors left: the one you initially chose (Door #1) and the other unopened door (Door #2).
Should you stick with your original choice (Door #1) or switch to the remaining unopened door (Door #2) to maximize your chances of winning the car?
The counterintuitive answer is that you should always switch. Switching gives you a 2/3 chance of winning the car, while sticking with your initial choice only gives you a 1/3 chance. It may seem odd, but the probabilities work out in favor of switching doors.
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