A robot wrestling tournament with 16 participants is taking place. The defending

Question

A robot wrestling tournament with 16 participants is taking place. The defending champion is expected to win a match with the probability of 0.84 regardless of the opponent, and matches outcomes are assuned to be independent. (a) The single elimination tournament requires 4 consecutive match wins to win the toumament. What is the probability that the defending champion wins the tournament? Round your answer to three decimal places (e.g. 98.765) (b) The defending champion won the tournament again and now accepts open challenges. What is the expected number of matches until this robot is defeated by a challenger? Round your answer to two decimal places (e.g. 98.76) c) After the t irst defeat the robot's o nts are e laced to more ne ble ones increasing the winnin o ability to .93 what is th prot at iity that nis robots rst ussis en th chale ge Round your answer to three decimal places (e.g. 98.765)

Explanation / Answer

The defending champion is expected to win a match with probability p = 0.84

a) he win all the four matches = p^4 = 0.84^4 = 0.498

b) Here p = 0.84

So the defending champion is expected to loss a match with probability 1- p = 0.84 = 0.16

So the expected number of matches until this robot defeated by the

chalengers = 1/(1 - p) = 1/0.16 = 6.25

c) After the replacement of joint parts of the robot , his winning chances increases upto 0.93.

so that the probability of he is loss a match is 1 - 0.93 = 0.07

So the probability that this robot's first loss is the 5th challenge = p^4 * ( 1 - p ) = 0.93^4 * 0.07 = 0052

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