Luck is 運 pronounced 'Raa-ku'
Luck is a chance happening, or that which happens beyond a person's control. Luck can be good or bad.
An example would be: If you take a Mathematics exam and you guess the answer there's a chance that you will be correct or wrong! This is a 'Lucky Guess'.
Subject: "How does a belief in luck change the way a person reacts to good or bad fortune?"
Simplify: When someone believes in a good or a bad fortune they also believe in Luck. Luck is beyond a persons control, like a fortune. Some people believe that if you're good you'll have a good fortune, therefore better luck.
Basically, if you believe in luck you believe in a good or bad fortune.
"If a Person believes in luck then they also tend to believe in a good or bad fortune"
That means that a person, depending on his/her belief will act differently towards luck. If you're Buddhist your beliefs tell you to be kind to others and therefore increasing your Luck (chance) for a better life!