1. One out of every 100 tax returns that a tax auditor examines requires an audit. Find the probability that the first audit is the 25th tax return the auditor examines. Distribution type: Probability:

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**Problem Statement:**

1. One out of every 100 tax returns that a tax auditor examines requires an audit. Find the probability that the first audit is the 25th tax return the auditor examines.

   - **Distribution Type:** ______________
   - **Probability:** ______________

**Explanation:**

This problem involves determining the probability of the first success (audit required) on the 25th trial when there is a constant probability of success on each trial. The distribution type typically used for this kind of problem is the geometric distribution.

To solve this:

- Let \( p \) be the probability that a tax return requires an audit, \( p = \frac{1}{100} = 0.01 \).
- The probability that the first audit happens on the 25th tax return is calculated using the formula for the geometric distribution:

  \[
  P(X = k) = (1-p)^{k-1} \cdot p
  \]

  where \( k \) is the 25th trial.

- By substituting the values,

  \[
  P(X = 25) = (0.99)^{24} \cdot 0.01
  \]

- Calculate to find the probability.
Transcribed Image Text:**Problem Statement:** 1. One out of every 100 tax returns that a tax auditor examines requires an audit. Find the probability that the first audit is the 25th tax return the auditor examines. - **Distribution Type:** ______________ - **Probability:** ______________ **Explanation:** This problem involves determining the probability of the first success (audit required) on the 25th trial when there is a constant probability of success on each trial. The distribution type typically used for this kind of problem is the geometric distribution. To solve this: - Let \( p \) be the probability that a tax return requires an audit, \( p = \frac{1}{100} = 0.01 \). - The probability that the first audit happens on the 25th tax return is calculated using the formula for the geometric distribution: \[ P(X = k) = (1-p)^{k-1} \cdot p \] where \( k \) is the 25th trial. - By substituting the values, \[ P(X = 25) = (0.99)^{24} \cdot 0.01 \] - Calculate to find the probability.
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