For problem choose what type of problem it is and solve using the binomial, geometric, or Poisson distribution.

A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Success with any opponent is independent of previous encounters. The player continues to confront opponents until defeated.

a) what is the probability mass function of the number of opponents confronted in a game?

b) what is the probability that a player defeats at least two opponents in a game?

c) what is the expected number of opponents confronted in a game?

d) what is the probability that a player confronts four or more opponents in a game?

e) what is the expected number of game plays until a player confronts four or more opponents in one sitting?