P(exactly two children are cured) (Round to three decimal places as needed.) g. Without using the binomial probability formula, obtain the probability distribution of the random variable X, the number of children out of three who are cured. X 0 1 2 3 P(X=x) (Round to three decimal places as needed.) Help me solve this View an example Get more help.
P(exactly two children are cured) (Round to three decimal places as needed.) g. Without using the binomial probability formula, obtain the probability distribution of the random variable X, the number of children out of three who are cured. X 0 1 2 3 P(X=x) (Round to three decimal places as needed.) Help me solve this View an example Get more help.
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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![### Probability and Statistics: Binomial Distribution
#### Problem Description:
Pinworm infestation, commonly found in children, can be treated with a drug that is effective in 92% of cases. Suppose that three children with pinworm infestation are given the drug. This problem aims to determine various probabilities related to the treatment outcomes.
#### Part (d): List Possible Outcomes
List the outcomes in which exactly two of the three children are cured. (Let S be a success and F be a failure.)
**Possible Outcomes:**
- SSF
- SFS
- FSS
(Use a comma to separate answers as needed.)
#### Part (e): Find the Probability
Find the probability of each outcome in part (d). Why are those probabilities all the same?
**Each Outcome Probability:**
\[ 0.068 \]
(Round to three decimal places as needed.)
**Explanation for Equal Probabilities:**
The probability is the same for each outcome because each outcome is the same.
#### Part (f): Probability of Exactly Two Children Cured
Use parts (d) and (e) to determine the probability that exactly two of the three children will be cured.
\[ P(\text{exactly two children are cured}) = 0.203 \]
(Round to three decimal places as needed.)
#### Part (g): Probability Distribution Using Binomial Formula
Without using the binomial probability formula, obtain the probability distribution of the random variable X which represents the number of children out of three who are cured.
**Table: Probability Distribution of X**
\[
\begin{array}{|c|c|c|c|}
\hline
X & 0 & 2 & 3 \\
\hline
P(X = x) & & & \\
\hline
\end{array}
\]
(Round to three decimal places as needed.)
#### Visual Explanation:
The graph (or table) given displays the distribution of the probability related to the number of children cured. The values in the first row represent the possible number of cures (0, 1, 2, and 3). The second row would contain the corresponding probabilities for each number of cures, which would be filled in after calculation.
- **X = 0**: Probability none of the children are cured.
- **X = 2**: Probability exactly two children are cured.
- **X = 3**: Probability all three children are cured.
This table](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4cf2595-fe80-4355-a077-fa7b5d3da7e9%2F2dec8031-ef43-4afe-9f74-c1f04f78f765%2Fkh53n6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Statistics: Binomial Distribution
#### Problem Description:
Pinworm infestation, commonly found in children, can be treated with a drug that is effective in 92% of cases. Suppose that three children with pinworm infestation are given the drug. This problem aims to determine various probabilities related to the treatment outcomes.
#### Part (d): List Possible Outcomes
List the outcomes in which exactly two of the three children are cured. (Let S be a success and F be a failure.)
**Possible Outcomes:**
- SSF
- SFS
- FSS
(Use a comma to separate answers as needed.)
#### Part (e): Find the Probability
Find the probability of each outcome in part (d). Why are those probabilities all the same?
**Each Outcome Probability:**
\[ 0.068 \]
(Round to three decimal places as needed.)
**Explanation for Equal Probabilities:**
The probability is the same for each outcome because each outcome is the same.
#### Part (f): Probability of Exactly Two Children Cured
Use parts (d) and (e) to determine the probability that exactly two of the three children will be cured.
\[ P(\text{exactly two children are cured}) = 0.203 \]
(Round to three decimal places as needed.)
#### Part (g): Probability Distribution Using Binomial Formula
Without using the binomial probability formula, obtain the probability distribution of the random variable X which represents the number of children out of three who are cured.
**Table: Probability Distribution of X**
\[
\begin{array}{|c|c|c|c|}
\hline
X & 0 & 2 & 3 \\
\hline
P(X = x) & & & \\
\hline
\end{array}
\]
(Round to three decimal places as needed.)
#### Visual Explanation:
The graph (or table) given displays the distribution of the probability related to the number of children cured. The values in the first row represent the possible number of cures (0, 1, 2, and 3). The second row would contain the corresponding probabilities for each number of cures, which would be filled in after calculation.
- **X = 0**: Probability none of the children are cured.
- **X = 2**: Probability exactly two children are cured.
- **X = 3**: Probability all three children are cured.
This table
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