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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