13. Eighty percent of trees planted by a woodlands conservation group survive. What is the probabilitu that: a. a. 10 of the 12 trees just planted will survive? b. at least 10 of the trees just planted will survive? b.
13. Eighty percent of trees planted by a woodlands conservation group survive. What is the probabilitu that: a. a. 10 of the 12 trees just planted will survive? b. at least 10 of the trees just planted will survive? b.
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 Problem on Tree Survival
**Problem Statement:**
Eighty percent of trees planted by a woodlands conservation group survive. What is the probability that:
**a.** 10 of the 12 trees just planted will survive?
[Answer Box: a.]
**b.** At least 10 of the trees just planted will survive?
[Answer Box: b.]
---
**Explanation:**
To solve this problem, you would typically use the binomial probability formula, as it is a problem dealing with success/failure outcomes.
The binomial probability formula is given by:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
Where:
- \( n \) is the number of trials (12 trees).
- \( k \) is the number of successful trials (e.g., 10 trees surviving).
- \( p \) is the probability of success on an individual trial (0.8 for this problem).
- \(\binom{n}{k}\) is the binomial coefficient.
**Calculation Steps:**
- **Part a:** Calculate \( P(X = 10) \).
- **Part b:** Calculate \( P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) \).
These calculations provide the required probabilities for each question.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38cbb8d5-b2e4-4062-be8a-b15364eb39dc%2F7aab2357-1802-4395-a5e2-48f3898facfc%2Fbkyukxv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Problem on Tree Survival
**Problem Statement:**
Eighty percent of trees planted by a woodlands conservation group survive. What is the probability that:
**a.** 10 of the 12 trees just planted will survive?
[Answer Box: a.]
**b.** At least 10 of the trees just planted will survive?
[Answer Box: b.]
---
**Explanation:**
To solve this problem, you would typically use the binomial probability formula, as it is a problem dealing with success/failure outcomes.
The binomial probability formula is given by:
\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]
Where:
- \( n \) is the number of trials (12 trees).
- \( k \) is the number of successful trials (e.g., 10 trees surviving).
- \( p \) is the probability of success on an individual trial (0.8 for this problem).
- \(\binom{n}{k}\) is the binomial coefficient.
**Calculation Steps:**
- **Part a:** Calculate \( P(X = 10) \).
- **Part b:** Calculate \( P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) \).
These calculations provide the required probabilities for each question.
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