Jessica & George's Riddle: Hint

...I have two questions for you. Is that okay?
Go ahead.
Who do these three boxes belong to? You, Jessica?
Well, yeah.
In other words, you know which colors are traps, right?
Yeah, of course.



Yeah, of course. I figured giving her a bit of a scare would make for a nice psychological warfare tactic.
Thanks. Those hints will be enough.

Jessica & George's Riddle: The red box has higher probability

It was you, George, wasn't it? You thought this puzzle up. Did the Monty Hall problem even exist in 1986?
Nope, not until 1990. It's a puzzle that already exists in Ange's world, so I thought it'd be okay to use it.
George ran me through the answer, but I was totally lost. Anyway, I don't get the details, but in this case, the odds of the blue box having the medal are about twice the odds of the red box having it.

Jessica & George's Riddle: They're both the same

It was you, George, wasn't it? You thought this puzzle up. Did the Monty Hall problem even exist in 1986?
Nope, not until 1990. It's a puzzle that already exists in Ange's world, so I thought it'd be okay to use it.
George ran me through the answer, but I was totally lost. Anyway, I don't get the details, but in this case, the odds of the blue box having the medal are about twice the odds of the red box having it.

Jessica & George's Riddle: The blue box has higher probability

Well... I... I just sorta...
Think back to the 15 slice cake that you found the almond in. If there was only one almond, the odds of winning were one in fifteen, right?
Yeah. One in fifteen.



Still, Ange, what if the servants were also eating the cake, and it started with 20 slices?
Huh?
This is a party, right? It's not fair that the servants don't get any cake, don't you think? So, let's say it was originally a 20-slice cake. The servants took out five slices, then redecorated it as a 15 slice cake and let you choose a slice. If so, what would your chances of choosing the right slice be?



However, the servants know where the almond is, so they chose five slives for themselves that had no almonds. In other words, they removed five losing slice. That would mean your chances of winning were one in 15, not one in 20.
...They took out losing slices, so it's obvious that the probability would go up.
Just now, Jessica did the same thing. Jessica removed one of the two boxes you didn't choose. In other words, the odds that the remaining box you didn't choose was the winner went up a bit, right?
Ahaha, I sort of get it, but not really...



Now I'm getting confused...
Actually, you really are incredible, Ange. Even though you're only six, you're trying to understand posterior probability, a concept in probability theory. Probability really is interesting. I'm sure you'll like it when you get into high school and college. Go and enjoy studying it all you can.