In two different lotteries, the exact same numbers were drawn. Although this is an amusing story, the reports in the media as if we are facing an event with a probability of one in trillions - are completely unfounded
Danny Hellman
In two fairly close lotteries, the first on Tuesday, September 21, and the second on Saturday evening, October 16, the exact same six numbers were drawn: 13, 14, 26, 32, 33 and 36. The main edition of Channel 10 reported the next day that the probability of such an occurrence is less than one in five trillion (five followed by 12 zeros). On the YNET website, the probability value 0.00000000000025 was attributed to the event. In the newspapers "Haaretz" and "Yediot Ahronoth" it is written that the chance of those six numbers coming up twice in a month is 1 in 4 trillion. Even if we agree that this is a rather interesting coincidence, it must be clarified that these estimates of improbability are without any reason!
In the Lottery Lottery used today, six different numbers in the range 1 to 37 must be guessed. The number of possible combinations is approximately two and a half million (2,324,784). Accordingly, the chance of any six numbers, including the winning combination from the previous draw, to win the next draw is around one in two and a half million. Under the assumption of a fair lottery, the probability of repeating exactly the same six numbers, in two consecutive draws, is nothing but this: approximately one in two and a half million.
Moreover, in the current case it is not really two consecutive lotteries, but two lotteries within about a month of each other. The lottery company conducts about ten lotteries in one month. The chance that during ten different lotteries there will be a repetition of the same combination of six winning numbers is approximately one in fifty thousand (1/51,662). It should be taken into account that a pair of lotteries constitutes one and only opportunity for matching, however, among a group of ten lotteries, 45 pairs are included for potential matching.
A question of definition
How can one explain the huge gap between the real probability values and the exaggerated probability values reported by the media? A main source of this type of error is a discrepancy between the event whose chances are sought to be estimated and the event whose chances are actually calculated. To avoid the error, one must pay attention to what exactly is the occurrence about which they are asking, and adjust the calculation to the language of the definition.
The probability that a particular six of numbers (for example 1-2-3-4-5-6) will come up in a single lottery is around 1 in two and a half million, and in two consecutive lotteries around 1 in five and a half trillion. However, the probability that any six numbers will win in a single lottery is 1 (certainly some vehicle will win), and in two consecutive lotteries - around 1 in two and a half million. Since the event that sparked the media response was the mere repetition of the same combination of six numbers, and not the repetition of a particular combination of six numbers, then any six of numbers - and not necessarily the one that actually came up - could fit the definition of the event.
The question is not what is the probability that the combination 36-33-32-26-14-13 will be won in two lotteries, then the answer is indeed less than one in five trillion, but what is the probability that any combination among the two and a half million possible combinations will be won in two lotteries, then the chance is twice as high Two and a half million.
change
A. In order to win the big lottery prize, the participant must correctly guess the composition of the six winning numbers from the range 1-37, as well as one additional number ("the strong number") from the range 1-8. The strong number drawn in the two lotteries in question was not the same. However, for the benefit of the believers (of all sects) it can be noted that in the first of the two draws, the number 1 was drawn as the strong number, and in the second draw - the number 2.
B. The number of possible combinations of six different numbers from the range 1 to 37:
third. The probability of repeating the same combination of six winning numbers during ten draws:
Danny Hellman, Department of Psychology, Tel Aviv University
14 תגובות
They work on you every day.
This whole business stinks.
Maybe one day we will get to hear how they worked on us, save your money and stay away from this magnificent factory.
Yoel: You forgot that you also need to fill in a strong number between 1-10, that is, the chance of winning the first prize in the lottery is 1 in 2.5 million to the value times 10 possibilities of the strong number. This means, 1 in about 25 million.
On the face of it, the calculation [chance of 1 in 2.5 million] is incorrect. First, because the number of correct guesses is less than one in 5 lotteries, and according to the financial data of the reconciliation plant, I understand that the number of columns filled in each single lottery exceeds the average of 3 million, which would have required an average of one winner each cycle.
In addition, the cost of each column is less than 2.8 NIS X the options = 7 million NIS. When my starting first prize is 5 million NIS, there is no chance of profit and the lottery company is not a layman either and in general tends to make a profit, how strange.
So instead of me scraping the gray cells in my brain, maybe Laman Dhu will consider it up-to-date
Coincidence or not, this was not the first time that the same numbers were repeated.
On 16.10 the same sixes returned in the lottery
On 27.10 the same numbers returned in lot 123
16.02.2011 They returned the same 4 chance lottery cards after the lottery!
I follow the lotteries and all returns were within a short range of dates, and this did not happen in previous years.
Although the chance that there will be repetitions of 6 numbers is 1:2 million, but if the same numbers were repeated in the same places, shouldn't it be worth doing a calculation with importance to the location?
The chance is much less high if you look at the question of what is the chance that such or a similar event will ever happen since the establishment of the Conciliation Plant, the chance increases after every month that passes and even if there was a difference of 12 draws between the events, the chance would also increase.
What is the chance that this event would have happened naturally in all the years of the peace process? The answer is about 1%
In short, unlikely
Brilliant!
Even if you bet on one number that was already there, the chance will be 2 in 2.5 million (XNUMX?)
But here we are talking about the fact that there are 45 options for couples, so it is as if you buy 45 different registration forms for the lottery in order to win.
Hello, the link you wrote does not work
Am I the only one who has the feeling that someone is now laughing at all the statistics and calculations? Obviously, if you control the lottery, the odds are 1, right?
Where are all the conspirators when you really need them?
A slightly more intuitive explanation for the last result:
The chance of winning the lottery is x. Therefore, if you do 10 draws, then after the first draw, the chance that x will come out in one of the remaining 9 draws is x*9 (it's not completely accurate, but since x is very small, it's pretty accurate). After the second draw the chance that x will come out in the remaining draws is 8x and so on.
Therefore, we accept that the chance that it will happen from an event whose probability is x twice within 10 draws is
0+1+2+3+4+5+6+7+8+9=45*x
2324784 / 45 = 51662
Hooray for probability!
I wrote about it on the Weizmann Institute's website:
http://www.weizmann.ac.il/zemed/net_activities.php?cat=1415&incat=1412&article_id=3672&act=forumPrint
So what does that mean?
That it is better to fill in numbers that already existed? (The chance is 1 in 50000 instead of 2 million!!)
It doesn't make sense because statistics have no memory