• In the arcade game Skee Ball, players roll a ball up a ramp and receive 10 to 50 points based on where the ball lands. Players will attempt to aim the ball to receive higher scores, which are more difficult to achieve based on size and location.However, if a ball is rolled randomly up the ramp, the probabilities of the ball landing in different scoring areas are not equal. Assume the following probabilities for each possible score:

• Score	10 Points	20 Points	30 Points	40 Points	50 Points
  Probability	0.50	0.25	0.15	0.07	0.03

• Assume that a player rolls three balls at random. a) What is the probability of a total score of at least 100 points? b) If the first ball scores 30 points, what is the probability of a total score of at least 100 points? c) Are the events "the first ball scores 30" and "the total score is at least 100" independent? Why or why not?? d) What is the expected total score? What is the variance of the score on one roll?