can anyone tell me the probability for winning this game?

[squall_zell]

hi everyone,

i registered on a site with a curious game, but i want to know the odds for winning it, i search google for answer me and then i found this forum via big-board.com... like this section is called probability... i would like to know if there are anyone who can answer me...

here's the thing,
a friend of mine told me about this comapany and the prizes they offer so we registered, the game is same sort of lottery but instead the common 49 numbers there are only 35, and instead 5 balls awarded there are 7, but to be the winner you just have to get 5 right... confusing?
please, if someone know how to do it in a calculator, tell me what's the chances for someone win the 5th, 4th, 3rd, 2nd and 1st prize?

i'm very thankful

[SumZero]

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).

[squall_zell]

well, thank you very much /images/graemlins/laugh.gif. it seems that i have plenty of opurtunnities for winning a prize /images/graemlins/wink.gif

i didn't understand very well what you meant with "If you set up this lottery", but like i said the lottery is from a company and their site is www.lotto.wesza.com (http://www.lotto.wesza.com), i think there is no problem giving it to you since you already know the probability... /images/graemlins/wink.gif

thank you, once more