1. Thank you!

2. Originally Posted by ScottWH
Thanks for your answers and patience, but I just don't get it. Maybe I'm not asking the question correctly. I would like to know what the odds are of anyone winning the daily drawing.

Doesn't it matter how many people sign the book? If one person signs the book the odds of someone winning has to be less than say if 1000 people sign the book. Correct? If this is a true statement, then how can the odds of winning for those people who signed the book be 1/1600?
You are correct!

The calculation: 1/1600 x 300/1600 is not the probability of someone winning.

The calculation as Link supplied them is approaching the problem from the point of view of a random club member, 'playing against the all other members' ie what is the probability that any random club member gets his name drawn and has signed in. I think your previous wording confuses people as to what you are really after.

Is this then what you mean?

Calculating the probability of someone winning [that is anyone on a given Monday], is better explained from the point of view of the club; what is the chance that the club will give away a prize on a Monday - and yes, this is strongly dependent on the amount of 'playing members' ie the book signers.

The chance depends on the participants: If nobody signs, its 0 and if everyone signs its 1. The probability is also additive, each of the individual book signers on Monday has a 1/1600 chance of wining but 'the probability of someone winning' is the combined probability of them all: 300/1600)

It can then be calculated as: (1/1600) x N booksigners

When 300 people sign-in, its already high: 300/1600 (and of course when everyone signs its 1/1600 x 1600 = 1600/1600: they will have to give away a prize).

3. So does an induvidual book signer have a 1/1600 chance of winning on Monday or is it (300/1600) * (1/1600)?

What is the difference in your two statments:

The calculation: 1/1600 x 300/1600 is not the probability of someone winning.
The calculation as Link supplied them is approaching the problem from the point of view of a random club member, 'playing against the all other members' ie what is the probability that any random club member gets his name drawn and has signed in.

The probability is also additive, each of the individual book signers on Monday has a 1/1600 chance of wining ....

4. I think there was a misunderstanding. Adding on to the Ecologist's comment, I hope to clarify this for you.

The probability of a specific person winning on Monday is:

That's for any random person and you do not know whether they signed the book or not.

The probability of the club giving away a prize is dependent only upon how many people out of the 1600 sign the book:

The probability of someone winning a prize, given that you know they've signed the book is:

Does that help?

5. Yes. THank you.