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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

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Calculate the odds

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