Connectivity of Graphs

[HallsofIvy]

I am Samir. I am new to this forum. I found the ongoing discussion about graphs interesting. I also had one question regarding connectivity in graphs.

"If a graph is connected with a given probablity say p, what is the probablity that its subgraph is also connected with same probablity"?

In other words, is there any method to determine the connectivity of a subgraph given the connectivity of its parent graph?

I would really appreciate any help in this matter.

Thanks

Samir