Here are the odds, by country. Rate of legal immigration doesn't seem to be a primary determinate for that country's odds. www.usagreencardlottery.org/green-card-statistics.jsp
Slight nit: you want to add http to that so it gets linkified.
Thanks for posting it. It's super-interesting. I always suspected the chance for my country (Australia) was _reasonably_ good. This bears that out. In fact it might even be higher (5%) than I'd expected.
That being said I tried like 6-8 times and never won. But that's not too surprising even at 1 in 20.
In fact I think I've only ever met one person who had won this. As it happened he was from Russia.
Not a lawyer, eligibility is based upon being born in a country with low immigration to the US. I neither Canada nor Mexico qualify although I can't find the exact list right now.
You go in the Pakistani queue. One of my friend who is an Indian citizen can apply because he was born in Kuwait while folks who were born in India cannot apply.
If you're married to an Australian (non-Pakistani), you can "cross-charge" your GC application to your spouse. This is true for employer-based GC, may apply to diversity visa as well.
I believe one of the reason for having that rule is to prevent people buying citizenship of some poor country and then use that to apply for the lottery.
Selecting by country of birth prevents those shenanigans.