when you are calculating the NPV of a project where there is a chance of failure, what is the correct formula? I’ve come across these 3 (i.e. questions 9, 10, and 28 from reading 66) and can’t seem to understand what the question is asking that would require the change in formula:

Ps: Probablility of success

Pf: Probability of Failure

C0: Original cash outlay at t=0

expected NPV = Ps* NPV of future cash flows (not counting C0) if successful + Pf * NPV of future cash flows (not counting C0) if unsuccessful - C0

or,

Expected NPV = Ps * NPV of all cash flows (including C0) if successful + Pf * NPV of future cash flows (including C0) if unsuccessful

or,

Expected NPV = Ps * NPV of future cash flows (not counting C0) if successful - C0

Any help?