[sakaeyellow]

"How does a belief in luck change the way a person reacts to good or bad fortune?"

I haven't read all the replies. But I guess the meaning of "a belief in luck" here means "whether one belives that luck exists or not" (運が存在すると信じるか)

My suggested translation is:

運が存在するという信念は、幸運の時または不幸の時に 、人の反応にどんな影響があるのか。