Calculate the odds
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Calculate the odds



Factorial in practice to help work out the odds of winning the UK Lottery

Factorial in practice to help work out the odds of winning the UK Lottery



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Calculate the odds Calculate the odds Presentation Transcript

  • Calculate the ODDS
    It’s not good news, I’m afraid.
  • Chance, Odds Probability
    The chance of something happening is also:
    The odds of something happening
    This is sometimes express as x to y
    The probability is sometimes said as an x in y chance of it happening
    Mathematics expresses these as a fraction.
  • Some rules of Probability
    Imagine rolling a dice
    What are the chances of rolling a given number?
    There are 6 faces
    The chance (with a perfect, regular dice) is
    Pretty simple, I hope
  • Dice Probability
    Probability calculations
    Chances of rolling number 4 = 1/6
    What are the chances of rolling 4 OR 2?
    Both have the same chance so
    The two outcomes can be added
    -> 1/6 + 1/6 = 1/3
    Still quite simple, I hope. The odds are better.
  • Dice probability
    What are the chances of rolling 4 twice?
    Here we have to multiply the chances
    -> 1/6 * 1/6 = 1/36
    You have a 1 in 36 probability of doing so. The odds are poorer.
    Let’s work out the Lottery chances
  • Imagine a lovely, shiny £1 coin
    What are the chances of winning the straight jackpot in the UK Lottery with a stake of £1?
  • Lottery rules
    There are 6 numbers from a possible 49
    No number can be picked twice
    You need all six to be a jackpot winner
    We are ignoring the bonus numbers
    The chances are calculated as a Probability
    Probability is expressed as a fraction
  • Lottery Probability
    You have chosen 6 numbers
    The odds of your first number being in the 6 winners is 6/49, then …
    There are only 5 winning numbers left and 48 possibilities
    So the chances of your second number being there is 5/48, then …
    And so on: 4/47; 3/46; 2/45; 1/44
  • Lottery Probability
    Recall, calculating rolling 4 then 2 on a dice:
    -> 1/6 * 1/6 = 1/36 (Multiply the individual odds)
    So, multiply individual odds with the lottery:
    -> 6/49 * 5/48 * 4/47 * 3/46 * 2/45 * 1/44
    -> 6*5*4*3*2*1 / 49*48*47*46*45*44
    -> 720/10068347520
    -> 1/13983816
    Not great news.
  • Clever Maths
    Those awfully clever mathematical types have worked out a formula:
    Where x = number of balls (49)
    Where n = number to pick for jackpot (6)
    ODDS = Factorial(x) ÷ (Factorial(n) * Factorial(x-n))
    -> Factorial(49) ÷ (Factorial(6) * Factorial(43))
    Example: Factorial(6) = 6 * 5 * 4 * 3 * 2 * 1
  • Bad news
    Despite the beautiful maths and applied geek
    The answer is still 1/13983816
    Don’t worry, if you bought a ticket every week for 268919.54 years you’d probably win the jackpot.