.in powerball they draw 5 white balls from the same drum,but the red powerball is drawn from it's own drum so you can have the same number twice in a single drawing.

Powerball simulator. I've lost $82,151 out of 100,000 plays.

http://ipse.mnstate.edu/Junk/PowerBall7.swf

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It's a random number set without replacement, according to Chas H. That gives n-1 for the second drawing, etc. IOW, previous drawings constrain the probabilities of the subsequent drawing to an incrementally smaller probability set.

If it is without replacement.

B

Thank You. I am not very familiar with power ball. The link provided by Kuan illustrates this well.

I have lost 91,376

thanks for the link, I'm still pulling for the $5000 wins somewhere in the year 2600 and 3000.

You're missing the main point. The powerball does not consist of seven draws. It's a SINGLE draw of seven balls. One event, not seven, as far as the probability is concerned.

You can only bet on the lot; you can't enter a bet once a few of the numbers have been drawn, so the fact that the probability of a particular ball gets better throughout the game does not affect your odds of winning, and doesn't affect the probability of a particular draw occurring. It doesn't even affect the odds of a given ball being in the drawn set, since all bets are closed before the first ball in the set is drawn.

This really isn't all that complicated. It does matter that the balls are drawn without replacement; this affects the sample universe only.

But since you can't enter a slip with a set of balls that are outside of the sample universe, this has absolutely no effect on your chance of winning.

This is where you are wrong. It *does* consist of 6 draws plus the draw for the powerball from a separate bin. The numbers drawn from a single bin constitute separate events and the calculation of the odds is done that way. Each drawing affects the subsequent draw by reducing the field.
The odds of drawing a number the first pick are 1/53, the odds of drawing that number the 6th pick (if it has not already been drawn) are 1/48.
What are the odds for a game as you envision it?

Let me know when you're allowed to bet mid-game, and then I will consider your hypothesis to have some merit.

Until then...

The rules of the game determine how betting is done, not the calculation of odds.
You've obviously run out ideas here.

I am "out of ideas" in the sense that there is only one, which has not been invalidated. In fact, I give proof above that the lottery draw is equivalent to any other random number generator with the same range.

I've studied statistics and probability. I'm not trying to pull a fast one.

The rules determine how betting is done, that is true. I think what Matt L (correct me if I'm wrong) meant is that you can't change your picked numbers in the middle of the game. Therefore, while the odds for each number drawn change as you draw and not replace, it does not matter for your odds, since you chose them all before the draw took place.

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In Tony Montana hispanic accent:

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Enough about me, how are you doing?

This is what I am saying, and exactly why I say that the entire set of numbers can only be considered as one event.

Each draw (the entire set of numbers) is an instance of an "independent, identically-distributed random variable." This term is so pervasive in probability theory that it is usually abbreviated "IID." Perhaps a Google search on this term will bring some enlightenment.

A random number generator could generate the same number more than once in a series of 6 numbers. The odds for picking a series of 6 numbers by random generator out of 53 is 1/53 to the 6th power. The odds of picking a series of 6 numbers out 53 by the method used in Powerball are 1/53 x 1/52 x 1/51 x 1/50 x 1/49 x1/48. Are you claiming the products of these two operations are the same?