Assume the geometric distribution applies. Use the given probability of success p to find the indicated probability. Find P(5) when p= 0.20. P(5) = (Round to five decimal places as needed.)

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**Geometric Distribution Probability Calculation**

**Question:**

Assume the geometric distribution applies. Use the given probability of success \( p \) to find the indicated probability.

Find \( P(5) \) when \( p = 0.20 \).

\( P(5) = \) \_\_\_\_\_ (Round to five decimal places as needed.)

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**Explanation:**

In this problem, we are asked to find the probability \( P(5) \) in a geometric distribution, where the probability of success on a single trial is \( p = 0.20 \). The geometric distribution models the number of trials until the first success.

The probability \( P(n) \) of obtaining the first success on the \( n \)-th trial is given by:

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

Substitute \( p = 0.20 \) and \( n = 5 \) into the formula to calculate \( P(5) \). Remember to round your final answer to five decimal places.
Transcribed Image Text:**Geometric Distribution Probability Calculation** **Question:** Assume the geometric distribution applies. Use the given probability of success \( p \) to find the indicated probability. Find \( P(5) \) when \( p = 0.20 \). \( P(5) = \) \_\_\_\_\_ (Round to five decimal places as needed.) --- **Explanation:** In this problem, we are asked to find the probability \( P(5) \) in a geometric distribution, where the probability of success on a single trial is \( p = 0.20 \). The geometric distribution models the number of trials until the first success. The probability \( P(n) \) of obtaining the first success on the \( n \)-th trial is given by: \[ P(n) = (1 - p)^{n-1} \cdot p \] Substitute \( p = 0.20 \) and \( n = 5 \) into the formula to calculate \( P(5) \). Remember to round your final answer to five decimal places.
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