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Thread: Math: Odds/Chance Calculation

  1. #1
    Baby Seal Clubber ElPietro's Avatar
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    Math: Odds/Chance Calculation

    Ok, I am struggling to find a link to answer my question and it's been 8 or 9 years at least since my last stats/finite math class. I used to be great at this stuff, but now I can't remember the formula/calculation.

    I'll give a simplified scenario:

    You roll a die once and you have a 1 in 6 chance of rolling a particular number.

    If you roll that die twice, my contention is your odds, or chance increases of rolling that exact number. I can't remember if this is the factorial function or simple multiplication or what.

    Basically, if you have to roll a "1" and you have one roll your odds are easily determined, but what if you have 10 rolls to roll a "1". Each roll the odds are the same, but the overall odds are increased. How do you quantify this?
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    Baby Seal Clubber ElPietro's Avatar
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    Oh and if you have a link to a site that shows/proves this that would be great as well.
    Deadlifts are like women, they'll hurt you everytime, but they'll also make you a man. - Me

    Friends don't let friends do dumbell kickbacks. - Me

    ElP is the smartest man in the world. - Gyno Rhino

    A low voter turnout is an indication of fewer people going to the polls. -- Dan Quayle

    If do right, no can defense. -- Mr. Miyagi

    Deep Thoughts by Jack Handey:

    I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they'd never expect it.

    Is there anything more beautiful than a beautiful, beautiful flamingo, flying across in front of a beautiful sunset? And he's carrying a beautiful rose in his beak, and also he's carrying a very beautiful painting with his feet. And also, you're drunk.

    Current FFFA Enforcer

  3. #3
    Baby Seal Clubber ElPietro's Avatar
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    Sorry, probability is 1/6, odds are 1/5, just correcting myself before someone else does.
    Deadlifts are like women, they'll hurt you everytime, but they'll also make you a man. - Me

    Friends don't let friends do dumbell kickbacks. - Me

    ElP is the smartest man in the world. - Gyno Rhino

    A low voter turnout is an indication of fewer people going to the polls. -- Dan Quayle

    If do right, no can defense. -- Mr. Miyagi

    Deep Thoughts by Jack Handey:

    I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they'd never expect it.

    Is there anything more beautiful than a beautiful, beautiful flamingo, flying across in front of a beautiful sunset? And he's carrying a beautiful rose in his beak, and also he's carrying a very beautiful painting with his feet. And also, you're drunk.

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  4. #4
    One crazy MOFO/Mail man
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    They independant bernouli trials so the probabilty of each event is multiplied to get the total probability. i.e. rolling a 1 with 1 die 10 times in a row is (1/6)^10
    w00t

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    Baby Seal Clubber ElPietro's Avatar
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    Actually, that's not what I asked, but I finally found a site that gave me the answer.

    It is Probability1 + Probability2 - (Probability1 x Probability2)

    So 1/6 + 1/6 - (1/6 x 1/6) Which I believe works out to 30.1 % versus the original 16.67%.
    Deadlifts are like women, they'll hurt you everytime, but they'll also make you a man. - Me

    Friends don't let friends do dumbell kickbacks. - Me

    ElP is the smartest man in the world. - Gyno Rhino

    A low voter turnout is an indication of fewer people going to the polls. -- Dan Quayle

    If do right, no can defense. -- Mr. Miyagi

    Deep Thoughts by Jack Handey:

    I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they'd never expect it.

    Is there anything more beautiful than a beautiful, beautiful flamingo, flying across in front of a beautiful sunset? And he's carrying a beautiful rose in his beak, and also he's carrying a very beautiful painting with his feet. And also, you're drunk.

    Current FFFA Enforcer

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    Senior Member Anthony's Avatar
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    I agree with the mailman. The probability of getting any number for each roll remains the same, but when matching with a previous roll, the probability decreases with each roll.

    You have three socks - one black and two white. If you close your eyes and pick two socks are you more likely to get a match, mismatch, or are the outcomes equal?
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    Steak and Eggs pusher's Avatar
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    Ok I think the way this works out is by calculating the complement of the successful event. What I mean is the formula is Pr(S) = 1 - Pr(Sbar).

    So in your example the pr of success is 1/6, the complement or prob of failure is 5/6.
    So if you roll the dice 10 times you get Pr(Sbar) = (5/6)^10 = 0.162. So the prob of success of at least 1 roll of 1, is 1 - 0.162 = 0.838.

    methinks...
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    Steak and Eggs pusher's Avatar
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    Yeah ELP you got it right.
    "The highest reward for man's toil is not what he gets for it, but what he becomes by it." -John Ruskin 1819-1900

    "He who fights monsters should see to it that in the process, he does not
    become a monster. And when you look into the abyss, the abyss also looks into
    you." - Nietzche

  9. #9
    Senior Member Anthony's Avatar
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    Oh, I think I misread. You want to determine the probability of rolling "1" within 10 rolls?
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    Baby Seal Clubber ElPietro's Avatar
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    Deadlifts are like women, they'll hurt you everytime, but they'll also make you a man. - Me

    Friends don't let friends do dumbell kickbacks. - Me

    ElP is the smartest man in the world. - Gyno Rhino

    A low voter turnout is an indication of fewer people going to the polls. -- Dan Quayle

    If do right, no can defense. -- Mr. Miyagi

    Deep Thoughts by Jack Handey:

    I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they'd never expect it.

    Is there anything more beautiful than a beautiful, beautiful flamingo, flying across in front of a beautiful sunset? And he's carrying a beautiful rose in his beak, and also he's carrying a very beautiful painting with his feet. And also, you're drunk.

    Current FFFA Enforcer

  11. #11
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    the probability of rolling a one at least once within 10 rolls is equal to 1-the product of the probabilities of not rolling it across all 10 rolls

    OR

    1-[(5/6)^10)]

    or about 84%

    /edit
    LOL i should have read all the responses first

    yeah, pusher has it right

    it gets more complicated if you want to do anything other than find the probability of rolling 1 at least once, but that'll do for that calculation
    Last edited by Relentless; 04-16-2004 at 01:05 PM.

  12. #12
    Baby Seal Clubber ElPietro's Avatar
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    Which question stupidhead? The socks?

    The odds of finding a matched pair are as follows.

    You cannot get a matched pair by picking a black sock, as there is only one of them.

    So to get a pair you must pick white both times.

    Your odds of this is 2/3 the first pull, and 1/2 the second pull.

    So it would be 2/3 * 1/2 or .667 * .5 = 33%.

    I think.
    Deadlifts are like women, they'll hurt you everytime, but they'll also make you a man. - Me

    Friends don't let friends do dumbell kickbacks. - Me

    ElP is the smartest man in the world. - Gyno Rhino

    A low voter turnout is an indication of fewer people going to the polls. -- Dan Quayle

    If do right, no can defense. -- Mr. Miyagi

    Deep Thoughts by Jack Handey:

    I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they'd never expect it.

    Is there anything more beautiful than a beautiful, beautiful flamingo, flying across in front of a beautiful sunset? And he's carrying a beautiful rose in his beak, and also he's carrying a very beautiful painting with his feet. And also, you're drunk.

    Current FFFA Enforcer

  13. #13
    Baby Seal Clubber ElPietro's Avatar
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    So to finish answering your stupid question, the odds are in favour of a mismatch, as less than half the time you will get a match in theory.
    Deadlifts are like women, they'll hurt you everytime, but they'll also make you a man. - Me

    Friends don't let friends do dumbell kickbacks. - Me

    ElP is the smartest man in the world. - Gyno Rhino

    A low voter turnout is an indication of fewer people going to the polls. -- Dan Quayle

    If do right, no can defense. -- Mr. Miyagi

    Deep Thoughts by Jack Handey:

    I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they'd never expect it.

    Is there anything more beautiful than a beautiful, beautiful flamingo, flying across in front of a beautiful sunset? And he's carrying a beautiful rose in his beak, and also he's carrying a very beautiful painting with his feet. And also, you're drunk.

    Current FFFA Enforcer

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    Pete I think you need to apply the same rationale to the sock question.

    you want to avoid the black sock, so your probability of success is equal to 1 - the product of your probabilities of failure across the two draws. You have the numbers right but the rationale wrong.

    Sock Draw #1: 1/3 chance of failure
    Sock Draw #2: 1/2 chance of failure

    probability of drawing a matched set of socks

    1-(.3333*.5)
    or
    83% chance of successfully dressing yourself with matching socks from that setup.

    I think

  15. #15
    Baby Seal Clubber ElPietro's Avatar
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    Bleh, not sure now that I think of it.
    Last edited by ElPietro; 04-16-2004 at 01:17 PM.
    Deadlifts are like women, they'll hurt you everytime, but they'll also make you a man. - Me

    Friends don't let friends do dumbell kickbacks. - Me

    ElP is the smartest man in the world. - Gyno Rhino

    A low voter turnout is an indication of fewer people going to the polls. -- Dan Quayle

    If do right, no can defense. -- Mr. Miyagi

    Deep Thoughts by Jack Handey:

    I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they'd never expect it.

    Is there anything more beautiful than a beautiful, beautiful flamingo, flying across in front of a beautiful sunset? And he's carrying a beautiful rose in his beak, and also he's carrying a very beautiful painting with his feet. And also, you're drunk.

    Current FFFA Enforcer

  16. #16
    Baby Seal Clubber ElPietro's Avatar
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    One thing though Cal, you don't need to draw the black sock twice, just once in either pull, so that may not be accounted in your calc.
    Deadlifts are like women, they'll hurt you everytime, but they'll also make you a man. - Me

    Friends don't let friends do dumbell kickbacks. - Me

    ElP is the smartest man in the world. - Gyno Rhino

    A low voter turnout is an indication of fewer people going to the polls. -- Dan Quayle

    If do right, no can defense. -- Mr. Miyagi

    Deep Thoughts by Jack Handey:

    I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they'd never expect it.

    Is there anything more beautiful than a beautiful, beautiful flamingo, flying across in front of a beautiful sunset? And he's carrying a beautiful rose in his beak, and also he's carrying a very beautiful painting with his feet. And also, you're drunk.

    Current FFFA Enforcer

  17. #17
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    yes but that's why the probability changes from pull one to pull two

    the black sock is the only thing that can create 'failure' therefore it is the relevant thing to measure

    you have a 1/3 chance of failure in pull 1 and a 1/2 chance of failure in pull 2

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    oh wait, yer right... the prob shouldn't be less than the 1/3 at the outset

    hm

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    I would fail my SATs if I wrote 'em today

    it's been too damned long since I've done stats

  20. #20
    Cyber Playa AllUp's Avatar
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    Quote Originally Posted by ElPietro
    Which question stupidhead?
    Classic.
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  21. #21
    Senior Member Anthony's Avatar
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    Socks = twice as likely to get a mismatch than a match.

    As for the dice, I know I'm rusty, but ... the probability of rolling a certain number is 1/6, so in theory by 6 rolls you should have rolled that number at least once ... so wouldn't the probability in 10 rolls be greater than 100%?
    Last edited by Anthony; 04-18-2004 at 11:20 AM.
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    Steak and Eggs pusher's Avatar
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    Quote Originally Posted by Anthony
    ... the probability of rolling a certain number is 1/6, so in theory by 6 rolls you should have rolled that number at least once ... so wouldn't the probability in 10 rolls be greater than 100%?
    In six rolls you could have rolled a 1 zero times, unless once you roll a number you can't roll that number anymore, but each event is independent.
    "The highest reward for man's toil is not what he gets for it, but what he becomes by it." -John Ruskin 1819-1900

    "He who fights monsters should see to it that in the process, he does not
    become a monster. And when you look into the abyss, the abyss also looks into
    you." - Nietzche

  23. #23
    Banned Reinier's Avatar
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    Quote Originally Posted by ElPietro
    Ok, I am struggling to find a link to answer my question and it's been 8 or 9 years at least since my last stats/finite math class. I used to be great at this stuff, but now I can't remember the formula/calculation.

    I'll give a simplified scenario:

    You roll a die once and you have a 1 in 6 chance of rolling a particular number.

    If you roll that die twice, my contention is your odds, or chance increases of rolling that exact number. I can't remember if this is the factorial function or simple multiplication or what.

    Basically, if you have to roll a "1" and you have one roll your odds are easily determined, but what if you have 10 rolls to roll a "1". Each roll the odds are the same, but the overall odds are increased. How do you quantify this?
    The chance you will throw a 1 at least once out of 10 rolls, is

    1-(5/6)^10

  24. #24
    Banned The_Brick's Avatar
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    You can't quantify it. In probability you can only give a probable estimate for a given event. Rolling a die ten times is 10 separate events. The probability is always 1/6 no matter what the previous results have been.

    By nature basic probabilty can only deal with events involving a Time (T) which is static. Obviously if we were to try and determine the probability of multiple events at multiple points (T) we would resort to using non-linear equations and venture into the world of quantumn probability.

    EDIT: It's the same with the roulette wheel you can't determine a red number will come up next simply because 5 black numbers have already turned up in a row. There will always be a 1/2 chance that it will be a black number again, although common sense might tell us otherwise.
    Last edited by The_Brick; 04-16-2004 at 10:50 PM.

  25. #25
    Banned Reinier's Avatar
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    Sounds nice but you are wrong. You CAN tell exactly how big the chance is to throw a 1 at least once in 10 throws. its

    1- (5/6)^10

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