(c) n=3, p=0.63, X=2 P (X) =
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
P(X) = ?
![The image contains a snippet from an educational platform's exercise on binomial probabilities. Below is a transcription and explanation suitable for an educational website:
---
**Progress Bar:**
- Part: 2 / 5
**Exercise:**
- Part 3 of 5
**Problem Statement:**
Calculate the probability for a binomial distribution with the following parameters:
- Number of trials (\( n \)): 3
- Probability of success on a single trial (\( p \)): 0.63
- Number of successes (\( X \)): 2
**Probability Calculation:**
\[ P(X) = \;[\text{Blank box for student input}] \]
---
### Explanation:
In this problem, you are asked to find the probability of achieving exactly 2 successes in 3 trials, with the probability of success on each trial being 0.63. This is a typical question involving the binomial probability formula:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
Where:
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \(\frac{n!}{k!(n-k)!}\).
- \( n \) is the total number of trials.
- \( k \) is the number of successes.
- \( p \) is the probability of success on each trial.
The student is expected to apply this formula to find \( P(X = 2) \) by substituting in the given values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b9b7f6a-cd0d-4490-81f2-bf1728b26b7f%2Fe5d39f83-4714-4600-85d3-665b7eb63b8c%2F7kxfn6r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a snippet from an educational platform's exercise on binomial probabilities. Below is a transcription and explanation suitable for an educational website:
---
**Progress Bar:**
- Part: 2 / 5
**Exercise:**
- Part 3 of 5
**Problem Statement:**
Calculate the probability for a binomial distribution with the following parameters:
- Number of trials (\( n \)): 3
- Probability of success on a single trial (\( p \)): 0.63
- Number of successes (\( X \)): 2
**Probability Calculation:**
\[ P(X) = \;[\text{Blank box for student input}] \]
---
### Explanation:
In this problem, you are asked to find the probability of achieving exactly 2 successes in 3 trials, with the probability of success on each trial being 0.63. This is a typical question involving the binomial probability formula:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
Where:
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \(\frac{n!}{k!(n-k)!}\).
- \( n \) is the total number of trials.
- \( k \) is the number of successes.
- \( p \) is the probability of success on each trial.
The student is expected to apply this formula to find \( P(X = 2) \) by substituting in the given values.
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