A robot wrestling tournament with 8 participants is taking place. The defending

Question

A robot wrestling tournament with 8 participants is taking place. The defending champion is expected to win a match with the probability of 0.78 regardless of the opponent, and matches outcomes are assumed to be independent. (a) The single elimination tournament requires 3 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) 0.475 (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 first defeat, the robot's joints are replaced to more flexible ones, increasing the winning probability to 0.87. What is the probability that this robot's first loss is the fifth challenge? Round your answer to three decimal places (e.g. 98.765)

Explanation / Answer

a) P(defending champion wins )=P(wins first ;second and third match)=0.78*0.78*0.78=0.475

b)

probability that robot is defeaed in a match p=1-0.78=0.22

expected number of matches until this robot is defeated =1/p=1/0.22=4.55

c)

P(robot;s fist loss is fifth challenge ) =P(wins first 4 and then wins 5th)=(0.87)4*(1-0.87)=0.074

( please try 0.081 if this comes wrong and revert)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.