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Gambling probabilities

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I will ask you a question.

"Which one of two is easier to guess. 10 numbers out of 35, or 25 numbers out of 35"
Phylosopher answer. Well... they both are the same. In first case you need to guess 10 lucky numbers out of 35. In second case you need to guess 10 unlucky numbers of 35. Thats true, since 35-25=10.


Mathematician answer.  Well... these are combinations. And combinations are calculated using equation:  In first case we get In second case we get And as you can see again - they both are the same.

I created also a graph showing where on X axes is count of numbers to guess, and on Y is probabiliy.

My advice to you is "DO NOT PLAY THESE KIND OF GAMBLING GAMES", because the probability is ridiculous. Let's look for example beloved 5 no 35 game. This game was created for total loosers. Chances that you will win the main prize is:

0,0000000000000000000000000000000000000103331%

ummm....