OT maths problem

2

Comments

  • cacbyname
    cacbyname Posts: 285
    When I was doing probability at school in Maths, I had an eccentric physics teacher at the same time who explained to us that all probabilities come down to a half - it can be a single coin toss, ten consecutive coin tosses, the odds of predicting the Grand National winner or of Elvis being found alive on the same day that aliens land in Trafalgar square. An event will either happen or it won't, hence the chance is always fifty:fifty.

    For those who've had a sense of humour bypass operation, he advised us to stick to conventional theory that leads to answers like 1/1024 for exams and gambling.
  • andrewgturnbull
    andrewgturnbull Posts: 3,861
    <blockquote id="quote"><font size="1" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by cacbyname</i>

    When I was doing probability at school in Maths, I had an eccentric physics teacher at the same time who explained to us that all probabilities come down to a half - it can be a single coin toss, ten consecutive coin tosses, the odds of predicting the Grand National winner or of Elvis being found alive on the same day that aliens land in Trafalgar square. An event will either happen or it won't, hence the chance is always fifty:fifty.

    For those who've had a sense of humour bypass operation, he advised us to stick to conventional theory that leads to answers like 1/1024 for exams and gambling.
    <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

    Wanna bet?
  • Phil Russell
    Phil Russell Posts: 1,736
    mmmmm... my wife is a maths teacher. She once asked a boy what he thought the chances were of winning the lottery. She said she could see the cogs whirring round as he thought about it. Finally he said '50 50'.
    Surprised, my wife asked why he thought that was correct...
    'Well', said the lad 'you either win or you lose'.

    And for all you would be mathematicians out there ... show me how, in a sample of about 30 people, the odds of two of them having the same birthday (month and date, not year) is about 50 / 50.

    Cheers, Phil
  • DaveyL
    DaveyL Posts: 5,167
    I can answer the snooker one - the probability is zero. If it's a break, at least one ball has been potted, so the balls cannot all end up in their starting positions...

    (I know that's not what you meant)
    Le Blaireau (1)
  • maddog_2cp
    maddog_2cp Posts: 73
    I'll give the answer to the birthday one in a minute but you might want to try this one in the meantime:

    Suppose you're on a game show, and you're given a choice of three doors.
    Behind one door is a car; behind the other two, goats.
    You pick a door - say, No.1 - and the host, who knows what's behind the doors, opens another door - say No.3 - which has a goat.
    He then says to you, "Do you want to pick door No.2?" Is it to your advantage to switch your choice?

    <font size="1"><font color="purple">
    Drop bars are a historical accident...... discuss</font id="purple"></font id="size1">
    Drop bars are a historical accident...... discuss
  • DaveyL
    DaveyL Posts: 5,167
    Yes! The probability it was behind door 1 was 1 in 3; the probability of it being behind either of the other two is 2 in 3.
    Le Blaireau (1)
  • maddog_2cp
    maddog_2cp Posts: 73
    very good

    Most people think it's 50:50 to switch, as the car is behind one of the two doors. So normally they say I'll stick with my first choice.

    The answer to the birthday one is 23 people by the way.

    Easiet way to undersytand it is if you start with one person in the room and add them one by one, and each time calculate the prob. that no match has been found

    Prob(no match) with just 2 people is 364/365 (if we assume birthdays occur on all days of the year equally)

    Prob(no match) with 3 people is 364/365 x 363/365 the third person must not match with either the first person or the second person

    Prob(no match) with 4 is 364/365 x 363/365 x 362/365

    and so on

    the calc for 23 people is prob(no match) = 0.493


    so for a room with 23 people there is a greater than 50% chance of a match

    when it reaches 60 people it's 0.994

    <font size="1"><font color="purple">
    Drop bars are a historical accident...... discuss</font id="purple"></font id="size1">
    Drop bars are a historical accident...... discuss
  • maddog_2cp
    maddog_2cp Posts: 73
    I should be working............

    <font size="1"><font color="purple">
    Drop bars are a historical accident...... discuss</font id="purple"></font id="size1">
    Drop bars are a historical accident...... discuss
  • DaveyL
    DaveyL Posts: 5,167
    The birthday one is a good one. I believe the "choose one from three, then have one wrong choice revealed to you" problem also comes up in the book "The Curious Incident of the Dog in the Nighttime" where the mathematical proof is also given. I could be thinking of another problem though.
    Le Blaireau (1)
  • cacbyname
    cacbyname Posts: 285
    <blockquote id="quote"><font size="1" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by andrewgturnbull</i>
    Wanna bet?
    <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
    As I said in the post: [:p]
    <blockquote id="quote"><font size="1" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by cacbyname</i>
    For those who've had a sense of humour bypass operation, he advised us to <b>stick to conventional theory that leads to answers like 1/1024 for exams and gambling.</b>
    <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
  • grimpeurcp
    grimpeurcp Posts: 3,043
    It is 1/1024 as other have said. Those who say 50:50 are idiots.

    We are talking about cascaded / cumulative probabilities.

    Consider it as a finite state machine. If you get a head, you progress to the next state, if not you reset to state one and start again. To get the required result you must make ten state transitions, the probability of each is 0.5. The probability accumulates at each state transition 0.5^10 = 1/1024

    For those interested, a technique based on this probability calculation, Maximum Likelihood Sequence Estimation, is used to perform error correction due to channel distortion in your mobile phone.
  • johndf
    johndf Posts: 250
    Glad to see Natureboyz has gone quiet. He needs to read the question again.

    Just in case you are there, Natureboyz, here is the question which I think you were answering. 'If a coin has already come up heads nine times in a row, what is the chance that it will come up heads next time?' This is totally different to the question which was asked.

    If you really were answering the original question as asked, then you have no understanding of probability. But that puts you in the same class as Professor Roy Meadows, who understands nothing about probability, (well statistical independence anyway), yet gets women convicted because apparently none else in court understood this simple concept either.

    As for the snooker question, the probability is zero, assuming that you can measure with perfect accuracy.
  • Mollie
    Mollie Posts: 90
    <blockquote id="quote"><font size="1" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by DaveyL</i>

    The birthday one is a good one. I believe the "choose one from three, then have one wrong choice revealed to you" problem also comes up in the book "The Curious Incident of the Dog in the Nighttime" where the mathematical proof is also given. I could be thinking of another problem though.
    <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Good book. I've also seen both that and the birthdays one in "The Magical Maze" by Ian Stewart (I think).
  • maddog_2cp
    maddog_2cp Posts: 73
    <blockquote id="quote"><font size="1" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">'If a coin has already come up heads nine times in a row, what is the chance that it will come up heads next time?'<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

    pay attention at the back please.


    all answers are available to those who read the whole post

    <font size="1"><font color="purple">
    Drop bars are a historical accident...... discuss</font id="purple"></font id="size1">
    Drop bars are a historical accident...... discuss
  • dave5ncp
    dave5ncp Posts: 3,198
    It was all revealed on Desert Island Discs

    <font color="purple"> <font size="1"><i>please pretend there's a horizontal line here. I couldnt work out how to put one in.</i></font id="size1"></font id="purple">
    You stir my natural emotions
    <font color="purple"> <font size="1"><i>please pretend there\'s a horizontal line here. I couldnt work out how to put one in.</i></font id="size1"></font id="purple">
    You stir my natural emotions
  • Actually, the proof of the "Monty Hall Problem" in <i>The Curious incident of the Dog in the Nighttime</i> is given in <b>graphical</b> form.

    It's the only way I've ever been able to understand it. Cause I'm a bit thick, me.

    Cheers,

    Tim

    http://vizarch.blogspot.com
  • John C.
    John C. Posts: 2,113
    On a similar note (well not really)

    'what is the air speed velocity of a swallow?'

    http://www.ripon-loiterers.org.uk/index.asp


    He who spins lasts longest
    http://www.ripon-loiterers.org.uk/

    Fail to prepare, prepare to fail
    Hills are just a matter of pace
  • Mister Paul
    Mister Paul Posts: 719
    I'm starting to get worried now. I can feel people edging towards the keyboard with thoughts of jet planes and conveyor belts. Please don't. Natureboys would explode trying to figure it out.

    __________________________________________________________
    <font size="1">Road Safety Expert</font id="size1">
    __________________________________________________________
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  • Jaded
    Jaded Posts: 6,663
    Ask him on a Friday night then. [:D]

    --
    <font size="1">[Warning] This post may contain a baby elephant or traces of one</font id="size1">
  • photojonny
    photojonny Posts: 382
    <blockquote id="quote"><font size="1" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by John C.</i>

    On a similar note (well not really)

    'what is the air speed velocity of a swallow?'
    <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

    A European swallow?

    where there's two wheels, there's a way....

    where there's two wheels, there's a way....
  • mr_hippo
    mr_hippo Posts: 1,051
    Possibly an African one but African swallows are non-migratory.


    http://bangkokhippo.blogspot.com/

    Ex-XXL weigh-in 26/27 May: Update published: Monday 28 May
  • Neilums
    Neilums Posts: 93
    <blockquote id="quote"><font size="1" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by John C.</i>

    On a similar note (well not really)

    'what is the air speed velocity of a swallow?'

    http://www.ripon-loiterers.org.uk/index.asp


    He who spins lasts longest
    <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

    Zero, if it's migratory.
  • I'm thinking of upgrading my tossing coin. Should I get a Shimano or Campagnolo?
  • maddog_2cp
    maddog_2cp Posts: 73
    toss off

    <font size="1"><font color="purple">
    Drop bars are a historical accident...... discuss</font id="purple"></font id="size1">
    Drop bars are a historical accident...... discuss
  • John C.
    John C. Posts: 2,113
    <blockquote id="quote"><font size="1" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by photojonny</i>

    <blockquote id="quote"><font size="1" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by John C.</i>

    On a similar note (well not really)

    'what is the air speed velocity of a swallow?'
    <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

    A European swallow?

    where there's two wheels, there's a way....
    <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

    African

    http://www.ripon-loiterers.org.uk/index.asp


    He who spins lasts longest
    http://www.ripon-loiterers.org.uk/

    Fail to prepare, prepare to fail
    Hills are just a matter of pace
  • maddog_2cp
    maddog_2cp Posts: 73
    now that's weird

    <font size="1"><font color="purple">
    Drop bars are a historical accident...... discuss</font id="purple"></font id="size1">
    Drop bars are a historical accident...... discuss
  • maddog_2cp
    maddog_2cp Posts: 73
    I've just done 10 numbers and it guessed every one. Include random numbers from my phone book.

    <font size="1"><font color="purple">
    Drop bars are a historical accident...... discuss</font id="purple"></font id="size1">
    Drop bars are a historical accident...... discuss
  • oldwelshman
    oldwelshman Posts: 4,733
    Yeah right. So how many times you won the lottery jackpot?
    The answer is as stated 1024 from 2 to the power of 10, simple.
    <blockquote id="quote"><font size="1" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by cacbyname</i>

    When I was doing probability at school in Maths, I had an eccentric physics teacher at the same time who explained to us that all probabilities come down to a half - it can be a single coin toss, ten consecutive coin tosses, the odds of predicting the Grand National winner or of Elvis being found alive on the same day that aliens land in Trafalgar square. An event will either happen or it won't, hence the chance is always fifty:fifty.

    For those who've had a sense of humour bypass operation, he advised us to stick to conventional theory that leads to answers like 1/1024 for exams and gambling.
    <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

    Feel free to browse and donate:
    http://www.justgiving.com/davidbethanmills
    My winter and summer bike pics

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  • cacbyname
    cacbyname Posts: 285
    Never won the lottery as I've never played it. I feel I pay enough tax already without making a voluntary contribution and I prefer to choose the beneficiaries of my charitable donations myself.

    Sounds like your operation was a success at least [:)]