### Understanding Geometric Distribution in Binomial TrialsIf a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the $ x $th trial is given by:\[ P(x) = (1 - p)^{x-1} p \]where $ p $ is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor (with blood group O and type Rh negative blood) is 0.07. ### Problem StatementFind the probability that the first subject to be a universal blood donor is the sixth person selected.\[ \text{The probability is} \ \](Round to four decimal places as needed.)### Steps to Solution- Identify the given parameters: - $ p $ (probability of success) = 0.07 - $ x $ (number of trials until the first success) = 6 - Apply the geometric distribution formula: \[ P(x) = (1 - p)^{x-1} p \] - Substitute the values into the formula: \[ P(6) = (1 - 0.07)^{6-1} \times 0.07 \] \[ P(6) = (0.93)^5 \times 0.07 \]- Calculate the probability: \[ P(6) \approx 0.6650 \times 0.07 \] \[ P(6) \approx 0.0466 \]### Final AnswerThe probability is approximately 0.0466.***Interactive Component:***- **Enter your answer:** You can type your answer directly into the provided answer box and click "Check Answer" to verify your solution.***Graph/Diagram:***There are no graphs or diagrams provided in the image. The content is focused entirely on the theoretical understanding and application of the geometric distribution in a binomial context.

If a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x) = p(1-p)*-1, where p is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor (with group O and type Rh negative blood) is 0.07. Find the probability that the first subject to be a universal blood donor is the sixth person selected. The probability is. (Round to four decimal places as needed.)

If a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x) = p(1-p)*-1, where p is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor (with group O and type Rh negative blood) is 0.07. Find the probability that the first subject to be a universal blood donor is the sixth person selected. The probability is. (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

### Understanding Geometric Distribution in Binomial Trials

If a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the $ x $th trial is given by:

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

where $ p $ is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor (with blood group O and type Rh negative blood) is 0.07.

### Problem Statement
Find the probability that the first subject to be a universal blood donor is the sixth person selected.

\[ \text{The probability is} \ \]

(Round to four decimal places as needed.)

### Steps to Solution
- Identify the given parameters:
- $ p $ (probability of success) = 0.07
- $ x $ (number of trials until the first success) = 6

- Apply the geometric distribution formula:
\[ P(x) = (1 - p)^{x-1} p \]

- Substitute the values into the formula:
\[ P(6) = (1 - 0.07)^{6-1} \times 0.07 \]
\[ P(6) = (0.93)^5 \times 0.07 \]

- Calculate the probability:
\[ P(6) \approx 0.6650 \times 0.07 \]
\[ P(6) \approx 0.0466 \]

### Final Answer
The probability is approximately 0.0466.

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***Graph/Diagram:***
There are no graphs or diagrams provided in the image. The content is focused entirely on the theoretical understanding and application of the geometric distribution in a binomial context.

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