Agree with Peter when referring to institutional brokers. However, would add a couple of comments regarding non-institutional, i.e. normal household investors. Your question really depends on what type of broker you are talking about, and what type of trading you are referring to.
If you are referring to simple online broking platforms targeting "mum and pop" investors i.e. everyday households, and if you are referring to speculative "day trading," by your average non-institutional investor, then chances are you are right, the broker is making money on each transaction, with next to no risk to them. Day trading works on the premise that the individual assumes the stock price will move, sometimes by relatively small amounts, either up or down, and trades the stock to make a profit. Simple online trading platforms do not provide sophisticated advice, or allow for sophisticated financial instruments, and hence make most of their money by taking little risk, and also hence a small cut of each transaction.