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A player of a video game is confronted with a series of opponents and has an 80%
Chapter 3, Problem 3-106(choose chapter or problem)
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. (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 two opponents in a game? (c) What is the expected number of opponents contested in a game? (d) What is the probability that a player contests four or more opponents in a game? (e) What is the expected number of game plays until a player contests four or more opponents?
Questions & Answers
QUESTION:
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. (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 two opponents in a game? (c) What is the expected number of opponents contested in a game? (d) What is the probability that a player contests four or more opponents in a game? (e) What is the expected number of game plays until a player contests four or more opponents?
ANSWER:Step 1 of 6
Given that a player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one.
If ‘p’ is the probability of success = defeat and ‘q’ probability of failure = victory then,
Also,
Also, Success with any opponent is independent of previous encounters. The player continues to contest opponents until defeated.
Let X be the number of opponents contested. This is the number of games played, including the last win which is lost.
This implies, X is a geometric random variable where the success of a player is defeating another player.