Question

A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Successwith any opponent is independent of previous encounters. Until defeated, the player continues to contest opponents. a. What is the probability mass function of

Answer 1

Explanation:

the probability mass function of number of opponents in the game

We have Bernoulli trail ("success" = defeat, "Failure" = Victory)

P = 0.20

We are "waiting" for our first "success" (Our first defeat) q = 0.80

X is Geometric Random variable.

P(X = x) = pq^(x-1) = (0.20)×(0.80)^(x-1) ................X≥1