a. Considering a success in a given case to be "a cure," formulate the process of observing which children are cured and which children are not cured as a sequence of three Bernoulli trials. Select the correct choice below and fill in the answer box within your choice.

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### Educational Resource on Probability and Treatment Effectiveness

**Problem Statement:**

Pinworm infestation, commonly found in children, can be treated with a drug. Suppose the drug has 80% effectiveness in curing the pinworm infestation, meaning it is successful in 80% of cases. Suppose that three children, with pinworm infestation, are given the drug. Complete parts (a) through (d) below.

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**Question:**

Considering success as a given case to be "cured," formulate the process of observing whether the children are cured as a sequence of Bernoulli trials. Select the appropriate description of a Bernoulli trial in the answer box with your choice.

**Choices:**
- **A.** Each trial consists of observing whether the child is cured of the pinworm infestation by the drug and has two possible outcomes, either not cured or cured. The results are independent.
- **B.** Each trial consists of observing whether the child is cured of the pinworm infestation by the drug and has two possible outcomes, either cured or not cured. The results are independent.
- **C.** Each trial consists of observing whether the child is cured of the pinworm infestation by other means and has two possible outcomes, which are cured or partially cured. The results are independent.
- **D.** Each trial consists of observing whether the child is cured of the pinworm infestation by the drug and has two possible outcomes, either not cured or cured. The results are independent. 

**Answer Box:** ☐

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**Explanation:**

- **Bernoulli Trial:** A Bernoulli trial is a random experiment where there are exactly two possible outcomes, often termed as "success" and "failure". The probability of success is the same every time the experiment is conducted, and trials are independent of each other.

- For the given problem:
  - The success probability (p) is 0.80 (since the drug is 80% effective).
  - There are two possible outcomes: "cured" (success) or "not cured" (failure).
  - Observations are done on each child separately and independently.
  
Based on the above definitions and problem conditions, the correct answer in the context of a Bernoulli trial would be **B**.

---

**Visual Aids:**

There are no graphs or diagrams provided in the image to explain further. The description above outlines the theoretical framework necessary to understand the process of observing whether
Transcribed Image Text:### Educational Resource on Probability and Treatment Effectiveness **Problem Statement:** Pinworm infestation, commonly found in children, can be treated with a drug. Suppose the drug has 80% effectiveness in curing the pinworm infestation, meaning it is successful in 80% of cases. Suppose that three children, with pinworm infestation, are given the drug. Complete parts (a) through (d) below. --- **Question:** Considering success as a given case to be "cured," formulate the process of observing whether the children are cured as a sequence of Bernoulli trials. Select the appropriate description of a Bernoulli trial in the answer box with your choice. **Choices:** - **A.** Each trial consists of observing whether the child is cured of the pinworm infestation by the drug and has two possible outcomes, either not cured or cured. The results are independent. - **B.** Each trial consists of observing whether the child is cured of the pinworm infestation by the drug and has two possible outcomes, either cured or not cured. The results are independent. - **C.** Each trial consists of observing whether the child is cured of the pinworm infestation by other means and has two possible outcomes, which are cured or partially cured. The results are independent. - **D.** Each trial consists of observing whether the child is cured of the pinworm infestation by the drug and has two possible outcomes, either not cured or cured. The results are independent. **Answer Box:** ☐ --- **Explanation:** - **Bernoulli Trial:** A Bernoulli trial is a random experiment where there are exactly two possible outcomes, often termed as "success" and "failure". The probability of success is the same every time the experiment is conducted, and trials are independent of each other. - For the given problem: - The success probability (p) is 0.80 (since the drug is 80% effective). - There are two possible outcomes: "cured" (success) or "not cured" (failure). - Observations are done on each child separately and independently. Based on the above definitions and problem conditions, the correct answer in the context of a Bernoulli trial would be **B**. --- **Visual Aids:** There are no graphs or diagrams provided in the image to explain further. The description above outlines the theoretical framework necessary to understand the process of observing whether
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