A rumor-spreading process evolves as follows. At time 0, one person has heard a rumor.

A rumor-spreading process evolves as follows. At time 0, one person has heard a rumor. At each discrete unit of time, every person who has heard the rumor decides how many people to tell according to the following mechanism. Each person flips a coin. If heads, they tell no one. If tails, they proceed to roll a fair die until 5 appears. The number of rolls needed determines how many people they will tell the rumor.

(a) After 4 generations, how many people, on average, have heard the rumor?

(b) Find the probability that the rumor-spreading process will eventually stop