Question for the math geeks only!

[sstimson]

ah lovely probability. I see five possibilities. 1) Jd killed in 1. 2) Jd killed in 2. 3)Jd not killed at all 4) Jd killed later than 2. 5)Jd killed at the start or before.

Any one of those possibilities have a 1 in 5 chance of being right and nothing can change that unless you cheat and there s more than one Jd.

so this way to your questions

1)You have No clue about how certain any one of the three people are, you only have their statements and each one can be false, so the question is, what is the chance of it being the first or second episode?

Then answer remains 1 in 5 or in your case 2 in 5. You take the number of cases (5) and then you take the number of outcomes you are looking at. In this case JD is either killed in Episode 1 (#1 above), or in Episode 2 (#2 above). There are only 2 cases here so the chances of JD being killed in either the 1st or 2nd Episode are 2 in 5.

2)And finally, suppose the number of people who believe Jd- was killed in the second episode increases exponentially, does that affect the chances ?

It does no matter if even the whole world believes Jd was killed in Episode 2. The chance he was is still 1 in 5.

[Kleene Onigiri]

You can only say it's "1 in 5" when you assume that the possibilities occur equally.
Like, the chance that Jd dies the first episode is a high as the chance Jd get's killed the 2nd episode. But you actually have no clue what the chances are, because that's actually the question that Conan324 stated: "You have No clue about how certain any one of the three people are, you only have their statements and each one can be false, so the question is, what is the chance of it being the first or second episode?"

So the actual possibility you can go with is: 1) Person A is right, Jd died Ep.1, 2) Person B is right, Jd died Ep. 2 3) Person C is right, Jd died Ep. 2 4) none of them is right, Jd didn't die at all (whatever)
So the question should be: "What is the chance that Person A is right?", for which you need the % chances of Jd dieing in episode 1 or 2 etc.

So that question how you formulated it, can't be solved without assuming too much.

[sstimson]

You can only say it's "1 in 5" when you assume that the possibilities occur equally.
Like, the chance that Jd dies the first episode is a high as the chance Jd get's killed the 2nd episode. But you actually have no clue what the chances are, because that's actually the question that Conan324 stated: "You have No clue about how certain any one of the three people are, you only have their statements and each one can be false, so the question is, what is the chance of it being the first or second episode?"

So the actual possibility you can go with is: 1) Person A is right, Jd died Ep.1, 2) Person B is right, Jd died Ep. 2 3) Person C is right, Jd died Ep. 2 4) none of them is right, Jd didn't die at all (whatever)
So the question should be: "What is the chance that Person A is right?", for which you need the % chances of Jd dieing in episode 1 or 2 etc.

So that question how you formulated it, can't be solved without assuming too much.

Sorry about this I going to give you an example where all three are right.

What if where A lives is very different where B lives. What if B and C live in a place that for some reason shown what was Episode 2 for A as Episode 1 for B & C. meaning that what A saw as Episode 1 became Episode 2 for B & C.

Now for my statements JD is either alive or dead and as I see it both are equally possible.
Next Jd was either killed Before the series began, was killed during the series or was alive and was killed
after the series was over. Again all are equally possible. Now lets put some letters in.
If JD is Alive we will use an A. If Jd is Dead a D. If Jd started an S. If Jd was killed at the end or after E and we use the number of the episode for 1 or 2.

That gives us this

Jd dead at start DS. Jd Alive at start AS.
Note that here it is one or the other. There is no middle ground and each is as likely as the other.

Jd dead at End ED. Jd Alive at End AE.
Note that here it is one or the other. There is no middle ground and each is as likely as the other.

a Define for the next step is needed. We need to remove my above example by defining it like this The Episode shall be the order in which there were made, NOT the order broadcast, or the order watched.

When Episode 1 was made either Jd was killed in it or no, again - Note that here it is one or the other. There is no middle ground and each is as likely as the other.
If Jd was killed in Episode 1 then that is 1D, otherwise 1A

When Episode 2 was made either Jd was killed in it or no, again - Note that here it is one or the other. There is no middle ground and each is as likely as the other.
If Jd was killed in Episode 1 then that is 2D, otherwise 2A

Now lets collect the possibilities. we have AS, DS, AE, DE, A1, D1, A2, D2

Now for our problem. AS, A1, A2, AE can all be true, but if Jd is dead then only one of the D's can be true.

Now lets look at each case and we start with the Jd dead cases

Dead at start os only DS is true, all others are false
Dead in Episode 1. Here both AS and D1 are true, the rest are false.
Dead in Episode 2. Here we get AS, A1, and D2 being true, the rest are false.
Dead at End. Thats makes AS, A1, A2, DE all true, the rest are false.
Also note that in these three cases AS appears three times. We could have one say AS, one say A1 and one say A2 and it is possible all are right.

But it remains that one and only one of the D's (DS, D1, D2, or DE) can be true if Jd died. this example removing all the alive chances and only dealing with the Dead ones. I see it this way either Did or Did not die is Episode 1 or 2 and yet again - Note that here it is one or the other. There is no middle ground and each is as likely as the other.

meaning in this example and removing the chance of Jd being still alive at the end means that one of four equal chances only two of then mach making it in the example 2 out of 4 or 1 in 2 chances that Jd dies in either Episode 1 or 2.

Now to deal that your three spoken persons

Person A is either telling the truth or lying - Again Note that here it is one or the other. There is no middle ground and each is as likely as the other.

Person B is either telling the truth or lying - Again Note that here it is one or the other. There is no middle ground and each is as likely as the other.

Person C is either telling the truth or lying - Again Note that here it is one or the other. There is no middle ground and each is as likely as the other.

Each of them have a 1 in 2 chances of telling the truth. Granted we are removing things like money, peer pressure, blackmail, ETC. This is just a simple example where IT IS ALWAY EITHER OE OF THE OTHER. It can not be that both Episode 1 and Episode 2 JD gets killed.

Simple. If Jd is killed in 2 he was alive in 1 and not killed. If Jd is killed in 1 he was dead in 2 and not killed.

[sstimson]

Here's another example that simplifies the problem i had in mind:

Consider the game show "who wants to be a millionaire", in the show, you have the option to ask the audience and each one of the audiences vote for the correct answer out of four possible answers. the contestant is then given the percent of how many people think each one of the answers is correct.

Assume that the answer "A" got 80% votes, what chance does it have of being the correct answer in the reference frame of the contestant?
my initial response was its 1 out of 4, since as sstimon said, it doesn't matter how many people believe which answer is correct, but only in the reference frame of the contestant.

But the "paradox" in this, is that the math suggests that asking the audience does not give the contestant any edge, when in real life, it obviously does, which makes me think the answer is wrong.

There is a reason for that. The idea is to assume that most people know that right answer and depending on the question that might be true, but remember that even if 95% say the same answer then they are either right or wrong so the chance the audience is right is 50% which is better the the 25% or the one in four answer being right. Once you choice an answer you too go from 25% to 50%. After all you are either right or wrong.