When a two-way paging system transmits a message, the probability that the message will be received by the pager it is sent to is p. When the pager receives the message, it transmits an acknowledgment signal (ACK) to the paging system. If the paging system does not receive the ACK, it sends the message again.
(a) What is the PMF of N, the number of times the system sends the same message?
(b) The paging company wants to limit the number of times it has to send the same message. It has a goal of P[N ≤ 3] ≥ 0.95. What is the minimum value of p necessary to achieve the goal?