Hay, on top of my CV ☺ here I tell you a little bit more about every day me. I like sports and exercise regularly. If you live in northern Helsinki, you could see me at the Malminkartano "Waste hill" more than once a week, on the steps which are about 425 pieces:). I believe that the hill is the highest place in Helsinki and on a clear day, from the top open some magnificent panoramas of the whole Metropolitan area. So please if you haven’t yet visited it welcome aboard and enjoy the views of our beautiful city-region at the best for your own schedule time ☺. I also exercise at home, mornings I do stomach movements, raise weights, do squat movements and exercise on a level. I also used to run a lot, but in 2009 I was involved in a severe car-accident in which I almost lost my life, and after that I had to adapt to the new reality at best with what was left of me. Fortunately what now is left from the crash, are several bad scratches and scars from the operations – 5 pieces.
During my financial analyst time at Kauppalehti, for 6 years I analyzed thousands of companies and even did as first- timer a good-will impairment test of a Publicly Listed Company - Trainer's House Oyj and thanks to my public challenge the company subsequently made more than 30 million € write-offs from its balance sheet in two subsequent years (2011 and 2012). If you are personally interested in the case send me a message and I can put you back the original calculations and the testing methodology of which l have given two lectures at the University of Applied Sciences Haaga-Helia.
But then here I made for you a special calculation of some interesting conditional probabilities of the Finnish lotto where for the prime reward you select 7 main numbers out of 39. Did you know that if we speak about the top prize, the probability that within the selected 7 prime numbers there will be at least 2 consecutive numbers is as high as 72.23% ☺? Or for example, that the probability that within the 7 selected numbers will be, let’s say, exactly one pair is equal precisely to 43.21% ☺. Well here I have developed for you a complete table-calculation, in which I have presented all possible probability results, regarding the sample distribution of the 7 selected numbers:
| N | Distribution | g (=n. elem.) | r (=n. elem. perm.) | Combin. | ((N-n)+1)! | g! | (33-g)! | Probab.% |
| 1 | 1+1+1+1+1+1+1 | 7 | 1 | 4272048 | 8.683E+36 | 5040 | 4.03E+26 | 27.77 |
| 2 | 2+1+1+1+1+1 | 6 | 6 | 6645408 | 8.683E+36 | 720 | 1.09E+28 | 43.21 |
| 3 | 2+2+1+1+1 | 5 | 10 | 2373360 | 8.683E+36 | 120 | 3.05E+29 | 15.43 |
| 4 | 3+1+1+1+1 | 5 | 5 | 1186680 | 8.683E+36 | 120 | 3.05E+29 | 7.72 |
| 5 | 2+2+2+1 | 4 | 4 | 163680 | 8.683E+36 | 24 | 8.84E+30 | 1.06 |
| 6 | 3+2+1+1 | 4 | 12 | 491040 | 8.683E+36 | 24 | 8.84E+30 | 3.19 |
| 7 | 4+1+1+1 | 4 | 4 | 163680 | 8.683E+36 | 24 | 8.84E+30 | 1.06 |
| 8 | 3+2+2 | 3 | 3 | 16368 | 8.683E+36 | 6 | 2.65E+32 | 0.11 |
| 9 | 3+3+1 | 3 | 3 | 16368 | 8.683E+36 | 6 | 2.65E+32 | 0.11 |
| 10 | 5+1+1 | 3 | 3 | 16368 | 8.683E+36 | 6 | 2.65E+32 | 0.11 |
| 11 | 4+2+1 | 3 | 6 | 32736 | 8.683E+36 | 6 | 2.65E+32 | 0.21 |
| 12 | 5+2 | 2 | 2 | 1056 | 8.683E+36 | 2 | 8.22E+33 | 0.01 |
| 13 | 6+1 | 2 | 2 | 1056 | 8.683E+36 | 2 | 8.22E+33 | 0.01 |
| 14 | 3+4 | 2 | 2 | 1056 | 8.683E+36 | 2 | 8.22E+33 | 0.01 |
| 15 | 7 | 1 | 1 | 33 | 8.683E+36 | 1 | 2.63E+35 | 0.00 |
| Sum | 15380937 | Sum | 100.00 |
Thus for example, the distribution of type 5+2 is one which has five consecutive numbers (ex. 23,24,25,26,27) and one pair (ex. 36,37) and out of the all 15 380 937 possible combinations there are exactly 1 056 pieces (0,01%) 5+2 ones☺. Then if you want to see the number of the possible combinations in which there is NO consecutive numbers, the type 1+1+1+1+1+1+1, (ex. 2,7,9,14,19,23,33), there are exactly 4 272 048 such combinations (27,77%) ☺! Or...there are exactly 33 combinations (0,0002%) where there are 7 subsequent numbers ☺, the first is 1,2,3,4,5,6,7 and the last is 33,34,35,36,37,38,39, the rest 31 are between them...this way you could check if my calculations work, but If you are interested in a more gentle way of how I calculated the probabilities send me a message. The solution is not directly in the textbooks ☺!
Well I hope that from the www.newfinns.com, you've already noticed that I like to travel and to take pictures, so if you have some time please do visit some of my trip-albums (Pictures of Rosti and then Pictures taken by Rosti), or please do not hesitate to listen some of the songs I like (Rosti’s music), it was difficult to choose “the best” tracks, but I hope that you like at least one of them☺!
Truly yours,
Rosti
Eurojackpot
Hello, yesterday (03.02.2015) I got a feedback from a member of the New Finnish and European generation that he wants to see the conditional probabilities of sequence of the Eurojackpot regarding the top prize and here I give you the solution:
|
N |
Distribution |
g (=n. elem.) |
r (=n. elem. perm.) |
Combin. |
((N-n)+1)! |
g! |
(46-g)! |
Probab% |
|
1 |
1+1+1+1+1 |
5 |
1 |
1370754 |
5.5E+57 |
120 |
3.34525E+49 |
64.70 |
|
2 |
2+1+1+1 |
4 |
4 |
652740 |
5.5E+57 |
24 |
1.40501E+51 |
30.81 |
|
3 |
2+2+1 |
3 |
3 |
45540 |
5.5E+57 |
6 |
6.04153E+52 |
2.15 |
|
4 |
3+1+1 |
3 |
3 |
45540 |
5.5E+57 |
6 |
6.04153E+52 |
2.15 |
|
5 |
3+2 |
2 |
2 |
2070 |
5.5E+57 |
2 |
2.65827E+54 |
0.10 |
|
6 |
4+1 |
2 |
2 |
2070 |
5.5E+57 |
2 |
2.65827E+54 |
0.10 |
|
7 |
5 |
1 |
1 |
46 |
5.5E+57 |
1 |
1.19622E+56 |
0.00 |
|
|
|
|
Sum |
2118760 |
|
|
Sum |
100.00 |
For the main prize in Eurojackpot first we select 5 main numbers out of 50 and then 2 additional numbers out of 10. Thus, the 5 main numbers can be selected in 2 118 760 different ways and the two additional numbers in 45 ways. Then for the jackpot (5 and 2) the number of all possible combinations is 95 344 200 (= 2 118 760 * 45). Hence speaking about the probability of the top prize we have 1/95 344 200 = 0.00001 per thousand (if you play with one combination☺). On the other hand, for example, the probability that the selected 5 prime numbers could contain a pair (ex. 7,8 (or another one out of the 49☺), distribution of type 2+1+1+1) is equal to 30.81% and etc. for the other alternatives.
Probably you have also noticed that compared to the Finnish lotto here the probability that within the 5 prime numbers there will be NO consecutive ones is as high as 64,70% (vs 27,77%), which said in simple language is due to the fact that we select fewer numbers (5) out of a larger initial set (50).
Kind regards,
Rosti
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