# Mathematical chance of winning local lotto



## Town (10 Feb 2009)

There are 28 numbers to choose from of which you must pick 4 only. What are the odds of it being won?


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## hizzy (10 Feb 2009)

You want to calculate your odds at winning the lottery given: 

You must choose a sequence of 4 numbers correctly to win.
The lowest number you can choose is 1
The highest number you can choose is 28
A given number can only be chosen *once* per try (per lottery ticket, etc.)
When you select your 1st number, you have 28 numbers to choose from, and... ...a 1 in 28 chance of picking the right one. (Mathematically, 1 in 28 is represented by the numerical fraction *1/28* or 0.035714.)​When you select your 2nd number, you have 27 numbers to choose from, and... ...a 1 in 27 chance of picking the right one. (Mathematically, 1 in 27 is represented by the numerical fraction *1/27* or 0.037037.)​When you select your 3rd number, you have 26 numbers to choose from, and... ...a 1 in 26 chance of picking the right one. (Mathematically, 1 in 26 is represented by the numerical fraction *1/26* or 0.038462.)​When you select your 4th number, you have 25 numbers to choose from, and... ...a 1 in 25 chance of picking the right one. (Mathematically, 1 in 25 is represented by the numerical fraction *1/25* or 0.040000.)​In order to win, you have to pick the first number right AND the second number right AND the third number right, etc. In the language of statistics, AND usually means to *multiply*. 
So, to figure out your odds of winning, multiply together all of the fractional odds of picking a given number correctly, as stated by the red fractions above. 
*1/28 × 1/27 × 1/26 × 1/25 = 1/491400* 
So, at this point, your odds of winning are 1 in 491400. But, since you can choose your winning numbers in any order, your chances of winning are somewhat better than this. Your chance betters by the number of different ways that a sequence of 4 numbers can be written down, which for 4 numbers is 4! (4 factorial) or 24. Divide 491400 by 24 to account for this, to get 20475. In other words, there are 24 different ways that the 4 numbers you choose can be filled out on your lottery ticket--if you choose your 4 numbers correctly, any of these ways will make a winning ticket.​That's it! You have a 
1 in 20,475 
chance of winning the lottery you described. (How do I pronounce this number?)http://www.webmath.com/cgi-bin/saynum.cgi?number=20,475

Here are some other odds for the sake of comparison: 

You have about a 1 in 2,000,000 chance of being struck by lightning.
A pregnant woman has a 1 in 705,000 chance of giving birth to quadruplets.
Someone eating an oyster has a 1 in 12,000 chance of finding a pearl inside of it.
Good luck! And sorry to say that the only way to increase your chances of winning is _to buy more tickets!_ Choosing birthdays, your age, addresses, years, phone numbers, etc. does not help at all!

Hope this helps​


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## Flexible (10 Feb 2009)

Very good, but I do it this way.

4 Numbers from 28

28 x 27 x 26 x 25 = 491,400 

491,400

Divided by 4, then 3, then 2 and then 1 = 20,475


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## demoivre (10 Feb 2009)

And on the calculator I press 28 nCr 4 which gives me 20,475 !


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## hizzy (10 Feb 2009)

Hi All

I just searched on the net for it. I personally wouldn't have a clue how to work it out.

Regards

Hizzy


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## macnas (10 Feb 2009)

all the calculations are using the same method.


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## car (10 Feb 2009)

youve a 50:50 chance.

you either win, or you dont.


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## Guest116 (10 Feb 2009)

car said:


> youve a 50:50 chance.
> 
> you either win, or you dont.


 
 You never got on too well with Maths then.


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## Eblanoid (10 Feb 2009)

car said:


> youve a 50:50 chance.
> 
> you either win, or you dont.



Do you work in the Department of Finance?


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## Town (16 Feb 2009)

Thanks all especially hizzy. Very well explained and easy to understand.


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## z103 (16 Feb 2009)

> youve a 50:50 chance.
> you either win, or you dont.


Buy two tickets.

Does this also apply to the National Lottery?


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## car (16 Feb 2009)

leghorn said:


> Buy two tickets.
> 
> Does this also apply to the National Lottery?



with 2 tickets youve 2 chances of winning but also 2 chances of losing so its still 50:50. 

The carsian formula applies to all lotteries/prize draws etc.


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## Guest116 (16 Feb 2009)

car said:


> with 2 tickets youve 2 chances of winning but also 2 chances of losing so its still 50:50.
> .


 
I actually thought you were joking before!


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## car (16 Feb 2009)

aristotle25 said:


> I actually thought you were joking before!



I was.


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## samanthajane (23 Feb 2009)

Eblanoid said:


> Do you work in the Department of Finance?


 
Just have to say this really made me laugh....... thanks


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