FWIW, if the odds are n : 1 and you draw n times, you will get one or more "hit(s)" 63% of the time.Ilovelottery wrote:Countifs is also great!
6/45 = 8 million tickets. 3N and above prize winnings tickets means just 2% are winning tickets. This = 1 in 42. Buy 20 tickets means 42/20 = 1 win in 2.1 attempts. But, you get 40 tickets, this means you win 1 in 1.2. This explains why you hit every time.
. . . . .
The formula is:
(( n - 1) / n)n
As it turns out, this is the odds of missing.
If n is 42, plug in the numbers to get:
((42 - 1) / 42)42
The result, using Windows calculator application in Scientific Mode is: 0.36345595217160275916620390978659
Since that is the odds of missing, the odds of hitting is:
1 - 0.36345595217160275916620390978659 = 0.63654404782839724083379609021341
If you draw twice the odds (84), the odds of getting one or more hits is 0.86789977083103360757339375653133
3 times (126) . . . 0.95198738542530638717269975296068
and so forth.
Upshot is, of course, the more draws the better your chances of "hitting". Also, no matter how many draws you make, there is always a chance of missing - unless you draw all possible combinations. And, no matter how few draws you make, you can still "hit".
There are two highly technical mathematical terms for the outcomes described in the previous paragraph. The two terms are: