Example 2

A pyramid-shaped token for a board game consists of congruent equilateral faces. Each face is a different color: blue, green, red, or white. Each face is equally likely to end up on the bottom if the token is rolled on the game board. What is the probability of the green face landing on the bottom? The probability of the same event occurring times is given by the function . Write a function for the green face landing on the bottom times in a row. Then, write the inverse of the function, and explain what the inverse function describes in the context of this problem.
  1. State the number of faces on the token.
  2. State the probability of any of the faces landing on the bottom.
  3. Check your answer to step 2 by calculating the chance that any of the faces lands on the bottom.
  4. Write the function for the green face landing on the bottom times in a row.
  5. Write the inverse of the function determined in step 4.
  6. Explain what the inverse function describes in the context of this problem.
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