### Probability of Seed GrowthIf a seed is planted, it has a 75% chance of growing into a healthy plant.If 10 seeds are planted, what is the probability that exactly 3 don't grow?[Input Box for Answer]---### ExplanationGiven a 75% chance of a seed growing into a healthy plant, it follows that there is a 25% chance that a seed won't grow. To solve for the probability that exactly 3 out of 10 seeds do not grow, you would use the binomial probability formula:\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]where:- $ n $ is the total number of trials (seeds planted)- $ k $ is the number of successful outcomes (seeds not growing in this case)- $ p $ is the probability of a success on an individual trial (probability that a seed does not grow)- $ \binom{n}{k} $ is the binomial coefficientIn this problem:- $ n = 10 $- $ k = 3 $- $ p = 0.25 $Thus, the probability that exactly 3 out of 10 seeds do not grow would be:\[ P(X = 3) = \binom{10}{3} (0.25)^3 (0.75)^7 \]### Calculation Steps:1. Calculate the binomial coefficient $ \binom{10}{3} $.2. Raise 0.25 to the power of 3.3. Raise 0.75 to the power of 7.4. Multiply all these values together to get the probability.Make sure to insert your answer in the provided input box.

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If a seed is planted, it has a 75% chance of growing into a healthy plant. If 10 seeds are planted, what is the probability that exactly 3 don't grow?

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

### Probability of Seed Growth

If a seed is planted, it has a 75% chance of growing into a healthy plant.

If 10 seeds are planted, what is the probability that exactly 3 don't grow?

[Input Box for Answer]

---

### Explanation

Given a 75% chance of a seed growing into a healthy plant, it follows that there is a 25% chance that a seed won't grow.

To solve for the probability that exactly 3 out of 10 seeds do not grow, you would use the binomial probability formula:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

where:
- $ n $ is the total number of trials (seeds planted)
- $ k $ is the number of successful outcomes (seeds not growing in this case)
- $ p $ is the probability of a success on an individual trial (probability that a seed does not grow)
- $ \binom{n}{k} $ is the binomial coefficient

In this problem:
- $ n = 10 $
- $ k = 3 $
- $ p = 0.25 $

Thus, the probability that exactly 3 out of 10 seeds do not grow would be:

\[ P(X = 3) = \binom{10}{3} (0.25)^3 (0.75)^7 \]

### Calculation Steps:
1. Calculate the binomial coefficient $ \binom{10}{3} $.
2. Raise 0.25 to the power of 3.
3. Raise 0.75 to the power of 7.
4. Multiply all these values together to get the probability.

Make sure to insert your answer in the provided input box.

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