A player of a video game is confronted with a series of 4 opponents and an 80% probability of defeating each opponent. Assume that the results from opponents are independent (and that when the player is defeated by an opponent the game ends). (a) What is the probability that a player defeats all 4 opponents in a game? Upper P equals left-parenthesis 0.8 right-parenthesis Superscript 4 Baseline equals 0.4096 (b) What is the probability that a player defeats at least 2 opponents in a game? Upper P equals 1 minus 0.2 minus 0.8 times 0.2 equals 0.64 (c) If the game is played 3 times, what is the probability that the player defeats all 4 opponents at least once? Probability defeats all 4 in a game = 0.84 = 0.4096. Probability defeats all four at least once = 1 – (1 – 0.4096)3 = 0.7942.
