Re #67, #70:
@tourdivoire, you are right. I'm not sure if it's the same in Australia, but in the U.S. there are small balls (they look like table-tennis balls) each with a different number printed on it. The balls are drawn at random, and once a ball is picked, it isn't returned to the collection. So, repetitions of numbers are not possible.
(In some smaller lotteries, there are a few groups of balls, each group containing 10 balls labelled 0-9. One ball is picked from each group, and so repetitions are possible here.)
I've never actually played lotto, so please feel free to correct me if I'm mistaken.
Absolutely not
@rachel8 !!!!
Sometimes in mathematics, we have to consider "spherical cows" for simplicity and
@tourdivoire #62 is a perfect example of this.
The probability is the same, when n ( the pool of numbers from which k numbers are drawn) is large enough.
In #62 example and for combinatorics as in Lotto, and for n sufficiently large, the probability of 11111 to be drawn ( with order not to be taken into account ) is the same as any other number like 123456 say ( again order doesn't matter ), which is approximately equal to 1/(n^6/6!) , for n sufficiently large. The actual number is 1 in (n+5)!/(n-1)!6!.
And this is exactly the same probability without repetitions allowed, as in Lotto, for very big n.
Thank you
@rachel8.
@psssssst ok I messed up because I didn't know repetitions were not allowed. Are you happy now?
Also spherical cows are a physicist's stuff. Not mathematics.
@tourdivoire The truth is, that you didn't mess up! Your example was brilliant! You still fail to understand that whether repetitions are allowed or not does not matter for large n.
So are you saying 0=1/45^6?
That's where we have to disagree, my friend.
It's not 0. You are playing two different kinds of lotto's. One with repetitions allowed and one without. When few numbers are to be drawn out of a very big lottery ( for example you are drawing 6 numbers out of 1-1000 range ), one case is the numbers you are drawing are not put inside the lottery again, the other is you put them back in, then the probability of any combination of 6 numbers 1-1000 drawn at random is the same.
It could be 11111 or 123456, it doesn't matter: the probabilities are the same.
Are you kidding me? Obviously if no repetition is allowed, then the probability to draw 1,1,1,1,1,1 is zero.
And the probability are not the same. They get closer and closer as n gets larger and larger, and they tend to zero as n tends to infinity.
<Comment deleted by user>
No!
Say, you want a certain combination of 6 numbers say: 1,500,54,87,999,111 to be drawn out of a lottery with 1000 numbers in it: 1-1000.
In the first case you draw a 1, you put it back in, draw a 500-- put it back, etc.
In the second case, you withdraw a number after it's drawn.
Then the probability of the given combination 1,500,54,87,999,111 is roughly the same in both cases. And this is exactly the probability as a 1,1,1,1,1,1 was drawn in the first case.
Look at #72 for a proof of this. You might like to evaluate the actual accurate probabilities as well, if you wish.
The probability to draw 1,1,1,1,1,1 with repetition allowed is 1/45^6, and it's the same as the probability lf drawing 1,2,3,4,5,6.
The probability to draw 1,1,1,1,1,1 if no repetition is allowed is 0 since 1,1,1,1,1,1 contains repetitions. It is not the same as the probability of drawing 1,2,3,4,5,6.
I see what you're trying to do here but it's not going to work with me. If you like to try and confuse other people, that's your problem.
