Is the National Lottery really random?

Posted by DBS
DBS
Born in England when black and white TV was a novelty in most homes, I have grow
User is currently offline
on Tuesday, 01 March 2011
in Digital Blogs

For several months now I have listened to the Natioinal Lottery results on a Sunday morning and every time is seems that there is a sequence or at least two consecutive numbers and given that you are pulling 7 balls (including the bonus ball) from 49 balls the chance of having consecutive numbers drawn each and every week is a little fishy but not impossible.

That didn't happen as badly last weekend. The Lottery plus numbers had 24 and 25 but that was all.

But look at the numbers listed in ascending sequence

Lottery:           10 19 24 27 39 49

Lottery Plus: 19 24 25 27 38 49

 

At first glance you see nothing out of the ordinary but remove the 10 from the Lottery numbers and the 35 from the plus numbers and you have 5 numbers that are the same.

Yes I will conceded that it is possible but the chances of it occurring are quite rare.

Using basic statistics (and I did cheat a bit as my brain had forgotten the formula) I calculated the number of possible combinations of choosing 5 numbers as 1,906 ,844 in other words you have a 1 in 1,906,844 chance of picking 5 numbers.

I will now concede that my statistics is very very rusty and will willingly accept criticism for the next calculation if I am wrong.

What then are the chances of getting 5 numbers the same in two consecutive lottery draws. this I believe is 1 in (1,906,844 X 1,906,844) or 1 in 3,636,054,040,336.

You have a better chance (1 in 750 000) of being struck by lightning than having what happened on 26th February.

So do you trust the organisers of the lottery?

 

Get subscribers

Add to Technorati Favorites

]]>

Tags: Untagged
DBS
Born in England when black and white TV was a novelty in most homes, I have grown up and dedicated my life to technology.

Came to South Africa in 1970 and completed formal education here.

I have used computer technology all my working life and still am learning more about using it everyday. The speed with which we can now share ideas and information is proof that the dreams and visions I heard in the late 1960's can come true

Comments

Dissol
Dissol
This time last year it was only February
User is currently offline
Dissol Tuesday, 01 March 2011

I think you make a mistake in your statistics...but as I employed a statistician to assist me on a project recently, I now know that I now nothing about statistics, and probability (but I think your figues give the probability for the same numbers, in the same sequence to be drawn). But the common error that we humans have is seeing a pattern, when in fact there isn't one. Yes, there is a slim possibility that all 5 numbers would match...but that doesn't mean it cannot happen. Because it is possible, if you do something enough times then you will see "unlikely" results. If you didn't see them sometimes, then it would be unusual... As humans we tend to get confused with probability. You will hear people saying things like "it's a miracle, the chances of this happening were only 1 in 3,636,054,040,336...but the fact that there are odds means that the event can happen...and to view it a miracle is to underestimate the number of things that happen all the time!...

The reason I say all this, is that while working with the statistician, I was reading a newspaper where an article was describing a woman who had won the big pay out in a lottery twice in one year, and I said that is remarkable. The statistician shrugged his shoulders and explained that it wasn't, and then spent half an hour bending my brain and showing me that actually, it was not that unusual...indeed he pointed out that it would be unusual if it did not happen. In fact, taking that lottery, he worked out that there should be a 50% chance that someone would win twice in any one year... I wish I could regurgitate his workings...it all made sense at the time!!

the new james rond
the new james rond
the new james rond has not set their biography yet
User is currently offline
the new james rond Tuesday, 01 March 2011

I sense you just want to win the Lottery Dissol. Easy money hey!

If you save Aus$10 each week (instead of buying the lotto ticket), starting at age 20 you would have accumulated AUS$500,000.00 (R3,500,000.00) when you reach 60. 100% guaranteed and this is a conservative estimate.

So trying to use stats to see if you get lucky is pie in the sky. Same as astrology and global warming all illusions. You should know better.

Doolally
Doolally
Doolally has not set their biography yet
User is currently offline
Doolally Tuesday, 01 March 2011

My youngest son asked me the one day "Why are they saying bye-bye chance bye- bye millions?", he was four at the time. This comment stuck with me as like you say the odds do seem a bit weird especially as we seem to be the only country that has consecutive numbers at every draw.

DBS
DBS
Born in England when black and white TV was a novelty in most homes, I have grow
User is currently offline
DBS Tuesday, 01 March 2011

@dissol I think my calculations are correct.
The sequence of the numbers does not matter so it is a combination with non repeating numbers so the formula in n!/( r!(n-r)!)
If the sequence did matter it a non repeating permutation and the formula is n!/(n-r)!
where n is the number you are choosing from and r is the number of numbers. If it was a permutation it would be 228,826,080
I mentioned my mind was rusty so I used this site http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html to assist

Simonwa22
Simonwa22
Simonwa22 has not set their biography yet
User is currently offline
Simonwa22 Wednesday, 21 September 2011

The lottery is completely random, it can't be fixed. I prefer playing the Lotto and Lotto Plus 5 compared to the EuroMillions as I think they've got better odds. You can play Lotto plus 5 here http://www.uk-lotto.com/lotto-plus-5.asp

Jawellnofine
Jawellnofine
Jawellnofine has not set their biography yet
User is currently offline
Jawellnofine Wednesday, 21 September 2011

humans are really a strange bunch.

There is always a conspiracy waiting to be manufactured. yet they will readily believe in something they can't see and be willing to kill for it.

Dissol
Dissol
This time last year it was only February
User is currently offline
Dissol Friday, 23 September 2011

@ DBS, I need to brush off my own mathematical rust too. But I do think your calculations are wrong. You are actually calculating that the chances of both sequences producing some of the same numbers...yes? But that is not what is happening...it is actually the second sequence managing to produce some numbers as the random sequence that appeared in the first. It sounds the same, but is actually different.

What I think this is, is an example of the "birthday paradox". It is called a paradox as it appears to be counter-intuitive. Take a random group of people and there is an apparently amazing chance that you will find people sharing the same birthday. The probability rises to 99% by the time that you reach only 57 people... The calculation for the probability is p=1-p(n). If you widen the parameter, then the if you take a random 6 people, then there is good chance that 2 of them share a birthday within a week. Of course this is different to a person having a specific birthday (which I would suggest is what you are calculating). As that would be 1/365.25 (remembering the leap year!).

I used to love maths...but I am soooooooooooo out of practice!!

Dissol
Dissol
This time last year it was only February
User is currently offline
Dissol Friday, 23 September 2011

@ James. I never play the lotto. In fact I have no interest in gambling at all. If I had to then I would probably choose (European) Roulette, as the odds are the best. The US version has much lower odds as the have not only a "0" but also a "00" which tilts the odds too much in favour of the house. Does anyone know what system is used in South Africa?

Please login first in order for you to submit comments