Hi Singh,
First, understand that TCAS is a backup system. Air traffic control is responsible for maintaining separation between planes. Generally there is no need for TCAS, because ATC does an excellent job. It is only when both ATC and TCAS break down at the same time that collision is possible. Even then, it is an extremely remote possibility.
Extremely remote possibilities do not bother most people. Most passengers and pilots can deal -- emotionally -- with the fact that there is one accident every three to five million flights. Accidents are rare enough that anxiety does not develop. But passengers who tend to be anxious seek ABSOLUTE control as the antidote. The problem is, absolute control does not exist. Even so, but many depend on the illusion that they are absolutely safe. When a passenger who depends upon an illusion of absolute control finds a flaw in the system, anxiety erupts.
Though it might seem that reassurance about this one issue is all that is needed, this is not the last issue that will come to mind. This process will continue. And, though aviation is remarkably safe, each fact that shows flying is not absolutely safe will cause anxiety.
Each such issue causes anxiety. As the number of these issues adds up, in time, anxiety builds up to the point that the anxious person becomes unable to fly.
Meanwhile, many people who recognize flying is not absolutely safe fly with little or no anxiety. This is due to their having good emotional strength, a built-in ability to regulate emotional response to life's challenges and uncertainties. A person whose emotions are well-regulate within does not need to have absolute safety to feel reasonably secure in the world, and is able to take reasonable risks. This said, I would suggest you take advantage of the means which have been developed to increase emotional strength, so that concerns about extremely remote combinations of events does not cause distress.
I have worked with anxious and fearful passengers since 1980, first with the course that was started in 1975 at Pan Am by Capt Truman "Slim" Cummings. Though those original courses -- and most currently operating courses -- are helpful only for mild flight anxiety, methods have since been developed for increasing emotional strength so that people with high to extreme flight anxiety and phobia can now fly.
If interested, I've posted a video on this at
http://www.youtube.com/watch?v=Zcx6ZsvKHSA