Chaotic Musical Chairs!

Discrete Mathematics Level pending

You play musical chairs with 24 other people. The game starts in the first round with 28 chairs. However, the game soon descends into chaos!

  • In Round 2, 4 people force themselves into the game.
  • In Round 4, 4 people leave the game.
  • In Round 6, 7 people join the game.
  • In Round 10, 11 people decide to stay seated on their chairs and stop playing, 5 people also join the game.
  • In Round 11, the 11 people return to the game with their chairs.
  • In Round 12, 13 people give up and leave the game.
  • At the end of Round 20, 8 chairs are stolen, but the game continues as normal.

The probability that you will win is \({\frac{a}{b}}\). What is the value of \({100\times\frac{a}{b}}\)?

Leave your answer as a decimal to 2 decimal places.

\(\textbf{Details and Assumptions}\)

Note: The events described above in bullet points occur in addition to the removal of a chair every round and other rules stated below.

In musical chairs, players have to sit down on a chair by the end of the round. If a player isn't able to find a chair to sit down on by the end of the round, they are eliminated from the game. Every round, a chair is removed. The game ends when there is only one chair remaining, and the winner is the player that sits on the final chair. Each player has an equal chance of finding a chair.

This question is part of the set Musical Chairs. If you liked this question, try some of the other questions as well!


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