The Math Doesn't Add Up

I have tried hard to understand how the Obama can reform health care and pay for 30 million uninsured people and do it all for less than $1 T over 10 years. Clearly, I am missing something - or am I. Here's what I tried to do just considering the 30 million and the cost to insure them. Insurance premiums for a pretty good plan might cost $10,000 a year - (low for the current average family rate). So, 30 million people at $10,000 per year is $300 Billion and over 10 years that is $3 Trillion. Even if we cut the premium in half to $5,000 per year - which is in line with current average costs for individuals - that is still $1.5 Trillion and this covers only the 30 million uninsured. These numbers don't include the cost of pre-existing conditions - how many of the 30 million have medical conditions, cancer etc, that require more expensive treatments not often covered or covered only sparsely under current insurance policies? Will these 30 million new insurees have to pay a co-pay? Is there some belief that by creating a pool of 30 million people the rates will be much lower?? Well, if that is the case then the answer is right before our eyes - allow companies and individuals to shop across state boarders and allow for interstate pooling of insurees - in like industries for example - and current rates would come down. Why do we need a government run health care program? With $1.5 to $3 trillion floating around why not let it go to the industry? I guarantee that administrative costs will be 50 to 70% lower in the private sector than in the government sector. The majority of Medicare/Medicaid waste is on the government side of the house not on the other side.