I was thinking about the Monty Hall problem and I thought of a possible intuitive explanation:
- You choose a door.
- Monty gives you the option of sticking with your original choice or instead choosing both of the other two doors.
- If you decided to switch (which now becomes an obvious choice), Monty first opens the door with the goat behind it (say, to add to the excitement), and then opens the other door.
My question then is, is this reasoning flawed? Is this even the same problem as before? Because now, choosing to switch from one door to two doors becomes quite obvious, and so does the $2/3^{rd}$ chance of winning the car on switching.
Best Answer
I cannot find a flaw in your reasoning.
My own reasoning (if you are interested).
Someone who sticks to his original choice will win if his original choice was correct.
Probability on that: $\frac13$.
Someone who switches will win if his original choice was wrong.
Probability on that: $\frac23$.