Chaeyeon is an up-and-coming dancer who has joined a televised dancing competition to help boost her career. Due to her impressive performance in the competition so far, a famous label has given her a promising deal: if Chaeyeon gets two successive wins in the upcoming clincher segment, they will sign her a seven- year contract regardless of how the rest of the competition turns out. Eager, Chaeyeon signs the deal, but soon learns that she needs to choose how the clincher segment will proceed. In this segment she will be facing against two other highly- rated dancers, Yena and Yuri, in a three-round dance battle. Each round consists of Chaeyeon competing against either of the two, but she can’t battle the same person consecutively. Therefore, she can compete with them in either of two successions: Yena – Yuri – Yena, or Yuri – Yena – Yuri. Chaeyeon knows that Yena is a much better dancer than Yuri. Which of the two successions should Chaeyeon choose to compete in? (HINT: Find a way to express the probability that Chaeyeon will win against Yuri, against Yena.) What is the probability that 100 tosses of a fair coin will result in 50 heads and 50 tails?
Chaeyeon is an up-and-coming dancer who has joined a televised dancing competition to help boost her career. Due to her impressive performance in the competition so far, a famous label has given her a promising deal: if Chaeyeon gets two successive wins in the upcoming clincher segment, they will sign her a seven- year contract regardless of how the rest of the competition turns out. Eager, Chaeyeon signs the deal, but soon learns that she needs to choose how the clincher segment will proceed. In this segment she will be facing against two other highly- rated dancers, Yena and Yuri, in a three-round dance battle. Each round consists of Chaeyeon competing against either of the two, but she can’t battle the same person consecutively. Therefore, she can compete with them in either of two successions: Yena – Yuri – Yena, or Yuri – Yena – Yuri. Chaeyeon knows that Yena is a much better dancer than Yuri. Which of the two successions should Chaeyeon choose to compete in? (HINT: Find a way to express the probability that Chaeyeon will win against Yuri, against Yena.) What is the probability that 100 tosses of a fair coin will result in 50 heads and 50 tails?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
Chaeyeon is an up-and-coming dancer who has joined a televised dancing
competition to help boost her career. Due to her impressive performance in the
competition so far, a famous label has given her a promising deal: if Chaeyeon gets
two successive wins in the upcoming clincher segment, they will sign her a seven-
year contract regardless of how the rest of the competition turns out. Eager,
Chaeyeon signs the deal, but soon learns that she needs to choose how the clincher
segment will proceed. In this segment she will be facing against two other highly-
rated dancers, Yena and Yuri, in a three-round dance battle. Each round consists of
Chaeyeon competing against either of the two, but she can’t battle the same person
consecutively. Therefore, she can compete with them in either of two successions:
Yena – Yuri – Yena, or Yuri – Yena – Yuri. Chaeyeon knows that Yena is a much
better dancer than Yuri. Which of the two successions should Chaeyeon choose to
compete in? (HINT: Find a way to express the probability that Chaeyeon will win
against Yuri, against Yena.)
What is the probability that 100 tosses of a fair coin will result in 50 heads and 50
tails?
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