this depends more on the criminal. it can be both i guess
It mostly depends on the serial killer. People like Ed Kemper don't seem to have planned on any specific victim and relied on circumstance.
But different killers work within different geographic locations so will change or adapt depending on the situation.
@Daniel Sumner oh, there is no pattern. Serial killers are choosing victims with a flow. In this case, Wrong time, wrong place may lead to death.