Offer your thoughts or opinion on the input financial query or topic using your financial background.

Estimate probability distribution of profit on investment 
There is no simple answer to that, because no one knows exactly what the probability distribution of S&P 500 returns is. Here is a sketch of one possible way to proceed. Don't forget step 4!  The problem is that the stock market is full of surprises, so this kind of "backtesting" can only reliably tell you about what already happened, not what will happen in the future.  People argue about how much you can learn from this kind of analysis.  However, it is at the least a clearly defined and objective process.  I wouldn't advise investing your whole nest egg in anything based just on this, but I do think that it is relevant information.