A binomial experiment with próbability of success p=0.21 and n=11 trials is conducted. What is the probability that the experiment results in 3 or more successes? Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.) 0 2 X
A binomial experiment with próbability of success p=0.21 and n=11 trials is conducted. What is the probability that the experiment results in 3 or more successes? Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.) 0 2 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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![The text reads:
"A binomial experiment with probability of success \( p = 0.21 \) and \( n = 11 \) trials is conducted. What is the probability that the experiment results in 3 or more successes?
Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)"
### Explanation:
This image presents a problem related to binomial probability. We are asked to calculate the probability of obtaining 3 or more successes in a series of 11 trials, where the probability of success for each trial is 0.21.
#### Steps to Solve:
1. **Understand the Binomial Probability Formula**:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
Where:
- \( \binom{n}{k} \) is the binomial coefficient.
- \( n \) is the number of trials.
- \( k \) is the number of successes.
- \( p \) is the probability of success on a single trial.
- \( (1-p) \) is the probability of failure.
2. **Calculate Probability for 0 to 2 Successes**:
Use the binomial formula to find probabilities for 0, 1, and 2 successes.
3. **Calculate the Probability of 3 or More Successes**:
Subtract the sum of probabilities for 0, 1, and 2 successes from 1.
4. **Round the Answer**:
Round the final probability to three decimal places.
This exercise requires using statistical concepts to solve a practical problem, aiding understanding of probability distributions in real-world scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2743f58a-999a-485c-8435-d316e3b49890%2Fe3845a96-a59a-462a-a9da-1ad9bfab67a0%2Fydb08v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The text reads:
"A binomial experiment with probability of success \( p = 0.21 \) and \( n = 11 \) trials is conducted. What is the probability that the experiment results in 3 or more successes?
Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)"
### Explanation:
This image presents a problem related to binomial probability. We are asked to calculate the probability of obtaining 3 or more successes in a series of 11 trials, where the probability of success for each trial is 0.21.
#### Steps to Solve:
1. **Understand the Binomial Probability Formula**:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
Where:
- \( \binom{n}{k} \) is the binomial coefficient.
- \( n \) is the number of trials.
- \( k \) is the number of successes.
- \( p \) is the probability of success on a single trial.
- \( (1-p) \) is the probability of failure.
2. **Calculate Probability for 0 to 2 Successes**:
Use the binomial formula to find probabilities for 0, 1, and 2 successes.
3. **Calculate the Probability of 3 or More Successes**:
Subtract the sum of probabilities for 0, 1, and 2 successes from 1.
4. **Round the Answer**:
Round the final probability to three decimal places.
This exercise requires using statistical concepts to solve a practical problem, aiding understanding of probability distributions in real-world scenarios.
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