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ssignment 5 x WileyPLUS Secure https://edugen.wileyplus.com/eduger/lti/main.uni PLUS Montgomery, Applied Statistics and Probability for Engineers, 7e PRINTER VERSION BACK SOURCES Reserve Problems Chapter 3 Section 6 Problem 1 A robot wrestling tournament with 32 participants is taking place. The defending champion is expected to win a match with the probability of 0.81 regardless of the opponent, and matches outcomes are assumed to be independent. on s (a) The single elimination tournament requires 5 consecutive match wins to win the tournament. What is the probability that the defending champion wins the tournament? Round your answer to three decimal places (e.g. 98.765). ion 5 (b) The defending champion won the tournament again and now accepts open challenges. the expected number of matches until this robot is defeated by a challenger? Round your answer to two decimal places (e.g. 98.76). What is on 6 (c) After the first defeat, the robot's joints are replaced to more flexble ones, increasing the winning probability to 0.9. What is the probability that this robot's first loss is the fifth chaillenge? Round your answer to three decimal places (e.g. 98.765). DS on.6 Click if you would like to Show Work for this question: Open Show Wonk Question Attempts: Unlimited SAVE FOR LATER SUIMIT ANSWER MapleNet Study 1000 PM /14/2018

Explanation / Answer

a)P(defending champion wins)=(0.81)5 =0.349

b)probability of losing p=1-0.81 =0.19

expected number of matches =1/p =1/0.19 =5.26

c)

P(first loss in fifth challenge)=P(first 4 games in win and 5 th loses)=(0.9)4*0.1=0.066

(please try 0.082 if above comes wrong and revert)

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