For this question, use the fact that if the probability of doing something is , then the probability of doing it times in a row is (assuming each action is independent). Also, use that if the probability of doing something is , then the probability of not doing it is 1 . Every year, a university hosts a darts tournament for completely beginner players. There are 100 contestants in the tournament. Steve is one of those contestants.

a) Suppose these players have a 10% chance of hitting the bullseye on each shot. What is the probability of a Steve hitting the bullseye three times in a row ?

b) What is the probability of Steve not hitting the bullseye three times in a row? For example, he could hit the bullseye twice but miss the third time.

c) What is the probability of all 100 contestants not hitting the bullseye three times in a row?

d) What is the probability of at least one of the contestants hitting the bullseye three times in a row?