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Invisiblemantis
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Re: Math paradox, whats the answer?t [Re: elax420] * 1
    #21199940 - 01/30/15 01:16 AM (9 years, 3 months ago)

100 replies to answer an Introduction to Statistics question that is not a paradox.

We'll get to the bottom of this eventually :sherlock2:


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Invisiblepsi
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Re: Math paradox, whats the answer?t [Re: elax420]
    #21199951 - 01/30/15 01:22 AM (9 years, 3 months ago)

Yeah I think theoretical computer science is considered a subset of discrete math. The courses I've taken involved lots of proofs involving various forms of induction and properties of natural numbers and so on, and once you get past that groundwork it begins to get more computer-relatable. Also there's a lot of boolean algebra type shit throughout.

Edited by psi (01/30/15 01:28 AM)

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Invisiblepsi
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Re: Math paradox, whats the answer?t [Re: mantis]
    #21199957 - 01/30/15 01:26 AM (9 years, 3 months ago)

Quote:

mantis said:
100 replies to answer an Introduction to Statistics question that is not a paradox.

We'll get to the bottom of this eventually :sherlock2:



Earlier in the thread I did my best to come up with sort of a paradox along similar lines to what the OP laid out.
http://www.shroomery.org/forums/showflat.php/Number/21191892#21191892

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Invisiblemantis
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Re: Math paradox, whats the answer?t [Re: psi]
    #21199964 - 01/30/15 01:29 AM (9 years, 3 months ago)

I can't work out a mathematical problem with an unspecified "mystery force" at hand. No offense :/


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Invisiblepsi
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Re: Math paradox, whats the answer?t [Re: mantis]
    #21199972 - 01/30/15 01:35 AM (9 years, 3 months ago)

I was going for a "proof by contradiction" kind of thing.

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Invisiblemantis
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Re: Math paradox, whats the answer?t [Re: mantis]
    #21199994 - 01/30/15 01:45 AM (9 years, 3 months ago)

I'm sorry, I think my response was a little dismissive. What is the weight of this force that "corrects" the probability of 10-in-a-row? It must use some kind of incremental probability to decrease the chance of tossing a consecutive heads or tails.

I think it would depend on the probability of the initial coin-flip. If it's 0.5 then you're more likely to break the 10 heads, 10 tails, 10 heads, etc. trend because 0.5 is more predictable than this:

S = same coin

01. p(S)=UNDEFINED
02. p(S)=1.0
03. p(S)=1.0
04. p(S)=1.0
05. p(S)=0.9
06. p(S)=0.9
07. p(S)=0.9
09. p(S)=0.9
10. p(S)=0.5

However, I'm tired, I just took a Klonopin, and I just threw some numbers in there and did not review this thoroughly. I just wanted to visualize your question.


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Edited by mantis (01/30/15 01:51 AM)

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Offlinestarfire_xes
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Re: Math paradox, whats the answer? [Re: mantis]
    #21200039 - 01/30/15 02:16 AM (9 years, 3 months ago)

The mathematics of why a coin flip is still 50/50 is explained by Random Walk. 

http://en.wikipedia.org/wiki/Random_walk


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Invisiblepsi
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Re: Math paradox, whats the answer?t [Re: mantis]
    #21200401 - 01/30/15 07:25 AM (9 years, 3 months ago)

Quote:

mantis said:
I'm sorry, I think my response was a little dismissive. What is the weight of this force that "corrects" the probability of 10-in-a-row? It must use some kind of incremental probability to decrease the chance of tossing a consecutive heads or tails.




What I was going for was showing that the idea of a coin that tries to avoid "unlikely" sequences in general (rather than just the specific case of long runs of the same thing) wouldn't really make sense, since any specific sequence is unlikely. I could throw a coin 40 times and get a seemingly random sequence, but then maybe it turns out that the sequence corresponds to the first 40 digits of pi in binary or something, and suddenly it seems extremely impressive.

I guess if you limit it to avoiding runs of the same thing though (rather than any sequence we as humans might find significant), the "mystery force" doesn't necessarily have to lead you to contradictory predictions.

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OfflineGorlax
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Re: Math paradox, whats the answer? [Re: starfire_xes]
    #21203196 - 01/30/15 04:08 PM (9 years, 3 months ago)

I mean isn't this obvious. Of course the coin toss is still 50/50. It will either land heads/tails. Nothing is weighing down one side making it an uneven ratio say 75/25.. The thing that is incorrect is the likely outcome given 10 coin tosses. The probability is not 50/50. People are confusing probability with odds of an outcome.

        (Chances for)
P(x) = ---------------
      (Total chances)

Switching it up and instead of coins using a deck of cards. The probability of drawing an ace in a single deck of
52 cards is

4/52 = 1/13 (or about 0.077 = 7.7%).

Odds, on the other hand, are given as:

    (Chances for) : (Chances against)

(Total chances) = (Chances for) + (Chances against)

You can deduce that ~~~~~~~~~
Chances against) = (Total chances) - (Chances for)
The odds of drawing an ace in a deck of cards is

4:(52-4) = 4:48 = 1:12


probability = (Total chances)
odds = (Chances against)

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OfflineAdolin
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Re: Math paradox, whats the answer? [Re: Gorlax] * 2
    #21203213 - 01/30/15 04:14 PM (9 years, 3 months ago)

the answer is 42

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InvisibleCognitive_Shift
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Re: Math paradox, whats the answer? [Re: Adolin]
    #21203228 - 01/30/15 04:20 PM (9 years, 3 months ago)

I'm not dweeby enough for this kind of stuff:tongue2:


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Offlinekoods
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Re: Math paradox, whats the answer? [Re: Cognitive_Shift]
    #21203286 - 01/30/15 04:35 PM (9 years, 3 months ago)

Here's a more challenging problem: what are the odds that in ten coin flips you get exactly five heads and five tails?


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NotSheekle said
“if I believed she was 16 I would become unattracted to her”

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Offlinezappaisgod
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Re: Math paradox, whats the answer? [Re: koods]
    #21203299 - 01/30/15 04:38 PM (9 years, 3 months ago)

You're a pain in the ass.


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Offlinekoods
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Re: Math paradox, whats the answer? [Re: zappaisgod]
    #21203306 - 01/30/15 04:40 PM (9 years, 3 months ago)

I guess you saw my dick pic. :rimshot:


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NotSheekle said
“if I believed she was 16 I would become unattracted to her”

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Offlinezappaisgod
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Re: Math paradox, whats the answer? [Re: koods]
    #21203346 - 01/30/15 04:53 PM (9 years, 3 months ago)

I did and it didn't look like it would be very painful.


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OfflineGorlax
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Re: Math paradox, whats the answer? [Re: zappaisgod]
    #21203400 - 01/30/15 05:03 PM (9 years, 3 months ago)

:ducklol:

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Offlinekoods
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Re: Math paradox, whats the answer? [Re: Gorlax]
    #21203500 - 01/30/15 05:24 PM (9 years, 3 months ago)

:lol:

BTW, I'm not quite sure how to calculate the odds myself.


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NotSheekle said
“if I believed she was 16 I would become unattracted to her”

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Offlinezappaisgod
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Re: Math paradox, whats the answer? [Re: koods]
    #21203504 - 01/30/15 05:25 PM (9 years, 3 months ago)

Yeah.  It was gonna take some work.  It is NOT a simple question.


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Invisiblepsi
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Re: Math paradox, whats the answer? [Re: zappaisgod]
    #21203644 - 01/30/15 05:44 PM (9 years, 3 months ago)

I can't think of how to go about systematically counting them up either. About 15 years ago I took a "Finite Math" course in high school that covered a lot of this kind of stuff. My first thought was to look at the middle number in the 10th row of Pascal's triangle.


So my guess is that out of 1024 sequences, 252 have 5 heads and 5 tails. Can't really give a good explanation why though.

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Offlinezappaisgod
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Re: Math paradox, whats the answer? [Re: psi]
    #21203664 - 01/30/15 05:49 PM (9 years, 3 months ago)

I have no idea what that is but if I was to start trying to figure it I would begin from the extremes and eliminate them one by one and detect a pattern.

Odds of all ten being x and go from there.  What's left is the answer.


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