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Calculate the odds

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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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Transcript

  • 1. Calculate the ODDS
    It’s not good news, I’m afraid.
  • 2. 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.
  • 3. 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
    1/6
    Pretty simple, I hope
  • 4. 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.
  • 5. 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
  • 6. Imagine a lovely, shiny £1 coin
    What are the chances of winning the straight jackpot in the UK Lottery with a stake of £1?
  • 7. 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
  • 8. 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
  • 9. 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.
  • 10. 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
  • 11. 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.