4.23 A student needs to know details of a class assignment that is due the next day and decides to call fellow class members for this information. She believes that for any particular call, the probability of obtaining the necessary information is 0.40. She decides to continue calling class members until the information is obtained. But her cell phone battery will not allow more than 8 calls. Let the random variable X denote the number of calls needed to obtain the information.

a. Find the probability distribution of X.

b. Find the cumulative probability distribution of X.

c. Find the probability that at least three calls are required.