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(10/06) Cecil Artavion : There are 3 possible outcomes after Shikamaru picks one of the exploding scrolls. Lets call the two exploding scrolls A and B. The three possible
outcomes are:
1. I first choose the scroll with no exploding note in it. I am then shown either scroll A or scroll B, which reveals an exploding note. If I change my choice of scrolls, I lose. If I stay with my original choice, I win.
2. I first choose scroll A. I am then shown scroll B, which has an exploding note in it. If I switche to the remaining scroll, I win. Otherwise, I lose.
3. I first choose door B. I am then shown scroll A, which has an exploding note in it. If I switche to the remaining scroll, I win. Otherwise, I lose.
>From the above choices I win 2/3 of the time when I switch scrolls as appose to winning 1/3 of the time with sticking with the choice I first had. I the obvious answer everytime I am faced with this choice is to switch scrolls.
Shika: Finally! Yes that is correct. Though I can only guess where the "door B" in your 3rd scenario came from... Still, as promised, you will eb the 1st one to enter our Hall fo Fame. Congratulations.
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(10/06) Annonymous : I'll consider things differently. First, I'll name the good scroll S1, the others S2 and S3.
There are 3 outcomes for this situation, that are the following :
1. We pick S1 the first time, if we switch, we lose.
2. We pick S2 the first time, if we switch, we win.
3. We pick S3 the first time, if we switch, we win.
All these possibilities have a probability of 1/3 of happening. We can easily see that out of 3 times, we win twice if we switch, and only once if we don't. We have a probability of 2/3 of getting the good scroll by switching. Therefore we should definitely switch scrolls.
One more time, Warbringer.
Shika: Surreal. Similar explanation that came shortly after the previous one too. But since you haven't seen the previous answer, yes you too, will enter Naruto Fever's Hall of Fame. Hit it on the 3rd try, ladies and gentlemen, we give you Warbringer :)
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