3.6.6 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. Until defeated, the player continues to contest opponents. What is the probability mass function of the number of opponents contested in a game? What is the probability that a player defeats at least two opponents in a game? What is the expected number of opponents contested 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?
3.6.6 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. Until defeated, the player continues to contest opponents. What is the probability mass function of the number of opponents contested in a game? What is the probability that a player defeats at least two opponents in a game? What is the expected number of opponents contested 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?
3.6.6 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. Until defeated, the player continues to contest opponents. What is the probability mass function of the number of opponents contested in a game? What is the probability that a player defeats at least two opponents in a game? What is the expected number of opponents contested 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?
3.6.6 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. Until defeated, the player continues to contest opponents.
What is the probability mass function of the number of opponents contested in a game?
What is the probability that a player defeats at least two opponents in a game?
What is the expected number of opponents contested 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?
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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Transcribed Image Text:A player of a video game is confronted with a series of opponents and has 80% probability of defeating each one. Success with any opponent is
independent of previous encounters. The player continues to contest opponents until defeated.
(a) What is the probability mass function of the number of opponents contested in a game?
(b) What is the probability that a player defeats at least 3 opponents in a game? Round your answer to two decimal places (e.g. 0.98).
(c) What is the expected number of opponents contested in a game? Round your answer to the nearest integer.
(d) What is the probability that a player contests 4 or more opponents in a game? Round your answer to four decimal places (e.g. 0.9876).
(e) What is the expected number of game plays until a player contests 4 or more opponents? Round your answer to the nearest integer.
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