First, I will assume that your client doesn't have a history of actually being assaulted and that his fears are not from PTSD. I will also assume that he does not live in a dangerous neighborhood (which might mean that his worries require constructive action to increase his safety - e.g. moving).

re: Probabilities

Your discussion about the probability of being accosted by going outside has the flavor of assessing the likelihood of an event with someone who has OCD.

I'd start by acknowledging the possibility of being accosted when leaving home and that staying home does, in fact, reduce that possibility. I'd also acknowledge that there is, in fact, genuine risk in going outside (as there is a possibility that you can get sick by touching a door knob and that we can never know FOR SURE that this won't happen).

A core issue for your client seems to be tolerance for uncertainty. Leaving our homes involves a willingness to live with the fact that an unlimited number of horrendous things can befall us when we venture into the world (e.g. 9/11 proved that a plane CAN fly into a building). Somehow, most people learn to live with this risk and not being 100% sure that something bad won't happen.

Jonathan Grayson points out that it's useful to distinguish uncertainty as a fact vs. uncertainty as a feeling. We all live with an infinite number of FACTUAL uncertainties all of the time. Try this thought experiment: Think of someone you dearly love and ask yourself if you know for sure that this person is still alive. Of course, you can call that person to check to make sure that he/she is ok, but how do you know that he/she didn't die as soon as you hung up the phone? YOU DON"T. So, as a fact, you spend most of your day living with the fact that loved ones can die at any minute. Distinguish these facts from the moments of FEELING unsure about specific possibilities.

You might ask the client what risks he takes when he is at home - there are many. Do you know how many people die every year from falling out of bed (there a surprising number!)? How about slipping in the shower and hitting your head? Ask the client to note that he, in fact, takes these risks all of the time.

Ultimately, one is faced with a cost/benefit analysis. What happens to your life and your goals when it is organized around minimization of all uncertainty and risk? Is that the life you want? How much of your avoidance of leaving home is actually about avoiding the FEELINGS of uncertainty and discomfort? If so, what are the costs of minimizing those feelings?

You might also ask the client how most people (not all) are willing to take the risk of leaving home. How does he imagine other people he knows might think about dealing with those risks?

Yes, leaving home requires courage. A life worth living involves taking risks. Otherwise, what kind of life do we have?