2023-12-21 21:00:00
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In Spain, every December 22, an event takes place that keeps a large part of the population in suspense, officially starting the Christmas celebrations: the Christmas lottery. It is a raffle in which 100,000 numbers are entered into a drum, of which only a few emerge as winners. These few winning figures are distributed between the First prizeknown as El Gordo, of 400,000 euros per tenth, the Second prizeof 125,000 euros, the Third of 50,000 euros, two Fourth Prizes of 20,000 euros, eight Fifth Prizes valued at 6,000 euros and, finally, a total of 1,794 Pedrea Prizes with only 100 euros per tenth.
If you do the math, you realize that only 13 numbers of those 100,000 They have large prizes of money – not to mention that the first three prizes are the goal of every lottery buyer – which represents a very small percentage. It is for this reason that many people consider it useless to “try your luck” in this type of games of chance, since the chances of winning become minimal. Now, is the probability really that low?
Kaprekar’s number: the mathematical amulet of the Christmas lottery
1 IN 100,000
Well, we can easily use mathematics to calculate how low – or high – the probability of winning the lottery is. As you may have already realized, playing with a single tenth does become a bit risky since you would be betting on one case in 100,000that is, the probability that your number comes out and is awarded the First, Second or Third Prize (for which there is only one number) would be only one 0,001 %. Now, since for the Fourth Prizes we have two winning numbers, in that case, your ticket would amount to 1 chance in 50,000what what gives you a 0,002% of probabilities of winning a Fourth Prize. Finally, if you opt for the fifth, then you would have a 0,008% of possibilities of winning a prize.
Lottery fever in the 18th century
However, in few cases a family faces the lottery with a single tenth. In fact, the more tenths you have, the greater the chance of winning in the draw. But how does that probability increase? Well in a way proportional to the number of tickets you have. That is, if with a single tenth your chances of winning the First Prize were reduced to 0.001%, with two tenths these will be 0,002%and with three tenths of the 0,003 %and so on progressively.
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Tenths of the Christmas Lottery of the year 2021.
MORE TENTHS, MORE POSSIBILITIES
Therefore, you can see that, indeed, the more tenths you have of different numbers, the greater your chances of winning. And if you think about it, if you have a single tenth and add up all your probabilities, those of winning each prize, you get that the percentage of your tenth being awarded in some way (without counting the stone, that is, only between the first prize or fifth prize) is 13 out of 100,000that is, of a 0,013%. The percentage is starting to go up, right?
Well now, imagine that you have, for example, 7 different numbers. In that case, your chances of one of your tickets winning one of the large prizes, that is, those that are not 100 euros, would be 0,091%. And if you have 20 tenths, your options reach 0,26 % probability of success!
It is true that the chances of winning are still really low, so it is reasonable that many people give up on this giveaway considering it unlikely. Now, if you want to continue maintaining hope, you must not forget that mathematics not only harms you, but also apply the same for everyone: all the previous winners started from the same statistics with which you face the draw this year. It’s just a matter of luck!
#probability #turn #mathematics