Coincidence - what is called coincidence and how to explain?

What you have given is a complicated coincidence. A simple coincidence will be like this. I have the programme of visiting a friend whom I have not seen for long time. I go to the market to buy some thing and I bang into my Friend there .As for your coincidence is concerned two people in fact many people get born on the same date but not at the same time. The difference in time of birth changes the life status but main features remain the same. Take the case of sri Ramaswamy mudaliar and Lakshmana swami mudaliar.They were twins and both became vice chancellors of Madras University.