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 contest opponents until defeated.
What is the probability that a player defeats at least two opponents in a game?
What is the probability that a player contests four or more opponents in a game?
What is the expected number of game plays until a player contests four or more opponents?
The Attempt at a Solution
I know that these are Bernoulli trials.
I chose Geometric distribution because the number of 'trials' is not fixed.
Defeat at least two opponents:
Contest four or more:
Expected games to contest four or more:
1/0.512=1.9?This is an illogical answer.