thesip2323MAY/CAN would only be redundant with CHANCE if they were talking about the same thing. It's redundant to say "There's a chance I may go" or "You may have a chance of winning." However, it might be okay to say "There's a chance that I can go," if it means that it MAY be possible that I am ABLE to go. In other words, CAN GO is talking about one thing (my ability to go, which may be simply binary--I can or I cannot), while CHANCE is talking about a possibility: maybe I can go; maybe I can't.
In this question, CHANCE is used to describe a probability. What is the chance that you will be injured in your home: 5%? 0.01%? Meanwhile, MAY/CAN is expressing a different idea: that this probability may (or may not) be equal to another probability--that of being injured in transit. So CHANCE X *may be* equal to CHANCE Y.