The document discusses calculating probabilities and odds. It provides examples of calculating the probability of rolling certain numbers on a dice, rolling certain numbers twice, and winning the lottery jackpot. The probability of winning the UK lottery jackpot by picking 6 numbers correctly out of 49 is calculated to be approximately 1 in 13,983,816.
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.
