1. The problem statement, all variables and given/known data 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? 2. Relevant equations f(x)=(1-p)^(x-1)*p E=1/p 3. 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: pmf(1)+pmf(2)=cmf(2)=0.2+0.13=0.36 Contest four or more: 1-cmf(3)=1-[pmf(3)+pmf(2)+pmf(1)]=1-0.488=0.512 Expected games to contest four or more: 1/0.512=1.9???This is an illogical answer.