Calculating the odds of matching 3 things out of 9

[Fayd]

So a local grocery store has a lame promotion right now where you get a card with 9 things to scratch off. You can only scratch off 3 and if you happen to get the right 3 that match, you win something.

First scratch you can get any of the winning 3 from the 9.
Second scratch you can get either of the remaining 2 from the 8.
Third scratch you have to get the last one from the 7

I haven't done statistics for years but to calculate that would you do:
3/9 * 2/8 * 1/7 which his about 1%?

Or is that wrong?

simple hyper-geometric model.

(3,3)(6,0)/(3+6,3) = 1/9c3 = 1/84

with this model i can also calculate the probability of getting 1 wrong, 2 wrong, and just completely fucking up.

(3,2)(6,1)/(3+6,3) = 3*6/84 = 18/84
(3,1)(6,2)/(3+6,3) = 3*15/84 = 45/84
(3,0)(6,3)/(3+6,3) = 1*20/84 = 20/84

 

[Rubycon]

What if you scratch all of 'em off and there's not even three - anywhere - that match? Can you sue for cheating? :biggrin:

 

[yhelothar]

No, there are 3 that match and 6 other random choices that do not match. There are not 3 set of 3. You have to get exactly the right 3 in order to win.

Gotcha.

 

[Baked]

Definitely but get a mechanism down to crack the lottery ones.

You would be surprised at what loops people will go through to get free money. :biggrin:

You're giving out too much information!