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 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? 0.16 (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). 0.64 (c) What is the expected number of opponents contested in a game? Round your answer to the nearest integer. 5 (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.
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 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? 0.16 (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). 0.64 (c) What is the expected number of opponents contested in a game? Round your answer to the nearest integer. 5 (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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 47E
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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?
0.16
(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).
0.64
(c) What is the expected number of opponents contested in a game? Round your answer to the nearest integer.
5
(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.
2
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