This is called conditioned probability. Imagine you toss a coin, and getting heads means winning. Now, getting 1000 heads in a row is very unlikely. You would
never bet you could make it, or you would bet, say, 1$ to 1000000$. Now you begin tossing coins and, and assume you get head... then head again... then head
again... 10 heads... 20 heads... (now you begin to feel *very* lucky)... finally you're at level 999 heads in a row. Is the 1000th head unlikely? Try to bet 1$
against 1000000$ for your 1000th head, no one will take the bet (unless they're statistical idiots). Your chances are now, plain and simply, 1/2. How come you have
50% probability of doing the very very unlikely 1000-heads sequence? Simple: because it takes a lot of luck to do 1000 heads, but you *already had* most of the
luck it needed. Now all you need is very little more luck: tossing a coin and getting a head, i.e., 1/2.
Door 2 and door 3 have equal conditioned probability of being the good one, i.e., 1/2.
A
Glenn Bradford ha scritto:
> Erin,
> Why don't you look up the word "teleology" in the dictionary and then
> directly quote where you think I've misrepresented its meaning, and why.
>
> What you said about coin tossing is correct but this will not help you
> with Rick's puzzle. I'm sorry but I don't understand your protests
> about my expanded version of the game. Having 100 doors is supposed to
> exagerate the effect that is hard to see with only 3 doors.
>
> When you choose door 57, you have to admit that you probably have it wrong.
> Nothing Monty subsequently reveals to you will change that, because you
> made the choice when you had less information. Monty then
> opens 98 doors showing booby prizes, purposely avoiding revealing the
> one with the good prize. So when only doors 57 and 66 remain, you can be
> nearly assured that 66 is the winner.
>
> I don't know if I can explain it any better. Sleep on it and go over what
> I wrote again tomorrow.
> Glenn
>
> Erin Noonan <enoonan@kent.edu> wrote:
>
> >Hi Glenn,
> >>
> >>
> >>By your reasoning, door number 57 has switched from having a 1%
> >>chance to a 50% chance for being the good prize because all those
> >>other doors are no longer an option.
> >
> >yes that is my reasoning, glad you were not as "creative" with it
> >as your definiton of teleology
> >
> >That's not sensible. Obviously you
> >>would switch. There's a 99% chance the good prize is behind door 66.
> >>Glenn
> >>
> >99%? now that's magic!
> >If he can guarantee that it is
> >behind door number 57 or 66 it is a 50% chance whether you switch or not.
> >You bringing the other doors is on the basis that Monty is a liar
> >and the probability is "really" based on 100 doors rather then 2.
> >I don't understand because you seem to believe Monty that it is
> >not behind the doors by your high 99% probability rate but at the same
> >time keeping the other doors in the equation because it might be
> >behind them? huh?
> >Like I said what I am reasoning on is my memory of coin
> >tosses. (i haven't double-checked but believe it is right)If you get
> >heads-heads-heads- heads whether you get heads again is 50 -50 it doesn't
> >decrease or increae because of past events.
> >The events of the other coin tosses don't affect the present coin toss.
> >The fact the first guess was 1/100 is independent thus does not affect his
> >second guess which is 1/2.
> >Monty offering switcheroos are irrelevent.
> >
> >so my reason is based on coin toss, where does yours come
> >
> >Erin
>
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