Who was correct?

アイドンノウくん · #1 June 25, 2014, 02:30 am

Once upon a time, three players, Inzanity, Petrol, and Psynix, were found guilty of fake bidding tws. Agatio had selected one of them at random to be pardoned. The warden, EvilTouch knew which one was pardoned, but was not allowed to tell. Inzanity begged the warden to let him know the identity of one of the others who was getting banned. "If Petrol is to be pardoned, give me Psynix's name. If Psynix is to be pardoned, give me Petrol's name. And if I'm to be pardoned, flip a fair coin to decide whether to name Petrol or Psynix."

The warden told Inzanity that Petrol was getting banned. Inzanity was pleased because he believed that his probability of getting pardoned had gone up from 1/3 to 1/2, as it was just between him and Psynix. Inzanity secretly told Psynix the news, who was also pleased, because he reasoned that Inzanity still had a chance of 1/3 to be the pardoned one, but his chance had gone up to 2/3.

Who do you think was correct? Inzanity or Psynix?

Eternalagony · #2 June 25, 2014, 03:43 am

Inzanity

ᴰᴱᴬᴰ† · #3 June 25, 2014, 06:40 am

Sleep

who came and banned them all

Drive · #4 June 25, 2014, 06:52 am

Quote from: dad

Sleep

who came and banned them all

LOL.

Balnazar · #5 June 25, 2014, 07:04 am

Quote from: IDuKnow

Once upon a time, three players, Inzanity, Petrol, and Psynix, were found guilty of fake bidding tws. Agatio had selected one of them at random to be pardoned. The warden, EvilTouch knew which one was pardoned, but was not allowed to tell. Inzanity begged the warden to let him know the identity of one of the others who was getting banned. "If Petrol is to be pardoned, give me Psynix's name. If Psynix is to be pardoned, give me Petrol's name. And if I'm to be pardoned, flip a fair coin to decide whether to name Petrol or Psynix."

The warden told Inzanity that Petrol was getting banned. Inzanity was pleased because he believed that his probability of getting pardoned had gone up from 1/3 to 1/2, as it was just between him and Psynix. Inzanity secretly told Psynix the news, who was also pleased, because he reasoned that Inzanity still had a chance of 1/3 to be the pardoned one, but his chance had gone up to 2/3.

Who do you think was correct? Inzanity or Psynix?

LOOOOL! Finally got to read a good "Once upon a time...." story, after a long time! xD

HellishKitty · #6 June 25, 2014, 07:04 am

Quote from: dad

Sleep

who came and banned them all

Dad was correct

by confusing them all

Sideris · #7 June 25, 2014, 09:59 am

Wait wait I've seen this somewhere already. Just, wherereee ngggh.
I know it's a mathematical paradox.

cevans1290 · #8 June 25, 2014, 10:08 am

Quote from: Sideris

Wait wait I've seen this somewhere already. Just, wherereee ngggh.
I know it's a mathematical paradox.

Yeah. some noob ( legit new person ) posted it.

USS Iowa · #9 June 25, 2014, 10:27 am

Inzanity obviously.

アイドンノウくん · #10 June 25, 2014, 01:53 pm

Well, it may seem intuitive that Inzanity was correct at first, but after considering below:

Pr(Inzanity pardoned AND Petrol's name was said) = P(Inzanity pardoned)*Pr(the coin decided to name Petrol)
=1/3 * 1/2 = 1/6

Meanwhile,
Pr(Psynix pardoned AND Petrol's name was said) = Pr(Psynix pardoned) since the warden must name Petrol in this case
=1/3 = 1/6+1/6

Above are the probabilities for ONLY the cases where the warden said Petrol's name to Inzanity.
The total probability of the warden telling Petrol's name = 1/6+ (1/6+1/6) =1/2

Inzanity was curious about his chance of getting pardoned after the warden said Petrol's name to him,
but Pr(Inzanity pardoned AND Petrol's name was said) = 1/6

Therefore, P(Inzanity pardoned AND Petrol's name was said)/P(Petrol's name was said)
= (1/6)/(1/2) = 1/3

This also means Psynix's chance of getting pardoned had gone up to 2/3 from 1/3, since Inzanity still had 1/3 to be pardoned, and he had to be in the remaining 2/3 of getting pardoned.

So, Psynix was correct, but only after Inzanity told him this GREAT news. Psynix's chance wouldn't have had gone up if Inzanity didn't ask the warden that question though.