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If you still cannot understand the Mounty Hall Problem, or you came from TikTok, I hope that this post is helpful.
Mounty what ? What is that ?
If you still don't know what is the Mounty Hall Problem, read this section :
A person presents you 3 boxes and tell you "one of them contains a Plush, and the rest of the two are completely empty (air molecules only), you can only choose one. And I know which box contains the Plush"
And so you picked one of them, that person then opens another box, it is empty inside, and then he ask: "Would you like to change your choice before you lock your choice ?"
Solution
Maybe you met this kind of question before, and maybe you know that you should change your choice, but you don't know why.
At the beginning, you might think that this has a 50% chance of getting the plush.
But let's think it this way:
Let's consider the four scenarios:
Scenario A (Lock) (Fail) :
You choose an empty box initially
You lock your choice,
you didn't get the Plush
Scenario B (Lock) (Success):
You choose a box with the Plush
You lock your choice,
you get the Plush
Scenario C (Swap) (Success):
you choose an empty box initially
you swap your choice,
the third box contains the plush.
Scenario D (Swap) (Fail):
You choose a box with the Plush
you swap your choice,
the third box is empty.
What is the probability for each scenario to take place if you lock your choice?
Scenario A (Lock) (Fail) : 2/3 (You start with an empty box)
Scenario B (Lock) (Success) : 1/3 (You start with a Plush box)
As you can see, if you lock your choice, you are most likely to fail.
What is the probability for each scenario to take place if you change your choice?
Scenario C (Swap) (Success) : 2/3 (You start with an empty box)
Scenario D (Swap) (Fail) : 1/3 (You start with a Plush box)
As you can see, if you change your choice, you are more likely to get the Plush.
One thing : there is just a higher probability to get the plush if you change your choice, but not it is not DEFINITE.
I hope this post helps, here's an image of a plush, good day (^w^)/
(any Vocaloid/MIKU fans here ?)
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