Re: can anyone tell me the probability for winning this game?
Yes someone can tell you the probability for winning this game. Did you want to ask a different question?
Assuming you only pick 5 numbers, the probability that the 5 numbers are amongst the 7 winning numbers is:
7C5 / 35C5.
That is there are 7C5 different sets of 5 winning numbers and there are 35C5 different ways of picking 5 numbers. (Where nCr = n!/((n-r)!r!)).
This is 21/324362 which is just a shade better than 1 in 15,500.
I don;t know what you mean by "second place" but if you mean matching 4 numbers etc. then the formula is:
7C4 * 28C1 / 35C5. (because 28C1 is the number of ways to not match 1 number).
More generally the formula for matching n numbers is 7Cn * 28C(5-n) / 35C5.
Hence you see that the probability of matching no numbers is about 30%. The probability of matching 1 number is about 44%. The probability of matching 2 numbers is about 21%. The probability of matching 3 numbers is about 4%. The probability of matching 4 numbers is about 0.3% (or about 1 in 331).
If you set up this lottery so that you sold tickets for $1 and you paid out $5000 for matching all 5 numbers, $100 for matching 4 numbers, and gave a free ticket to anyone who matched either 0 or 3 numbers then you'd have a lottery that would have an $EV of about $0.031 per ticket (for the lottery organization -$0.031 for the player).
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