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

•1/6• 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.