Ray Allen, who is one of the best 3-point shooters over the last 15 years in the NBA, has a chance to shoot four free throws.

Ray Allen, who is one of the best 3-point shooters over the last 15 years in the NBA, has a chance to

shoot four free throws. He was fouled shooting a 3-point shot, and he gets to take a fourth shot due to a

technical foul. Suppose that the probability that he makes a free throw is .9, and his free throws are

independent of each other. Let X be the random variable that gives the number of free throws made in 4

attempts.

a) Give the possible values for X. What type of distribution model is appropriate? Explain why.

b) Obtain the probability distribution for x.

c) Indicate what the probability is for Ray Allen to make three or more of the free throws.