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A player of a video game is confronted with a series of opponents and has 77%...

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Statistics

A player of a video game is confronted with a series ofopponents and has 77% probability of defeating each one. Successwith any opponent is independent of previous encounters. The playercontinues to contest opponents until defeated. (a) What is theprobability mass function of the number of opponents contested in agame? (b) What is the probability that a player defeats at least 3opponents in a game? Round your answer to two decimal places (e.g.0.98). (c) What is the expected number of opponents contested in agame? Round your answer to the nearest integer. (d) What is theprobability that a player contests 4 or more opponents in a game?Round your answer to four decimal places (e.g. 0.9876). (e) What isthe expected number of game plays until a player contests 4 or moreopponents? Round your answer to the nearest integer.

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