11:55 Find the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18%. p=[?]% Round to the nearest tenth of a percent. Enter
11:55 Find the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18%. p=[?]% Round to the nearest tenth of a percent. Enter
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![### Probability Problem on Binomial Experiment
#### Problem Statement:
Find the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18%.
#### Given:
- The number of trials (\(n\)) = 5
- The probability of success in any one trial (\(p\)) = 18% (0.18)
**Question:**
\[ p = [ \ ? \ ] \% \]
**Instructions:**
Round to the nearest tenth of a percent.
**Input Section:**
A blank text box is provided for input, followed by an "Enter" button to submit the response.
### Graphs and Diagrams:
There are no graphs or diagrams in this assignment; it is purely a textual problem dealing with a binomial experiment.
To find the requested probability, you would typically use the binomial probability formula or a cumulative binomial probability table:
\[ P(X \leq k) = \sum_{i=0}^{k} \binom{n}{i} p^i (1-p)^{n-i} \]
where:
- \( \binom{n}{i} \) is the binomial coefficient
- \( X \) is the random variable representing the number of successes
- \( k \) is the maximum number of successes (which is 2 in this problem)
By applying the values into the formula, you can calculate the required probability.
**Remember:** This is a critical concept in the study of probability and statistics, particularly useful in understanding experimental outcomes and their likelihoods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c912c6-a327-4873-9511-a364c6ae7474%2F026c70e9-e14a-4dc1-b2bf-ed2f81c5c31d%2Fjbaf7r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Problem on Binomial Experiment
#### Problem Statement:
Find the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18%.
#### Given:
- The number of trials (\(n\)) = 5
- The probability of success in any one trial (\(p\)) = 18% (0.18)
**Question:**
\[ p = [ \ ? \ ] \% \]
**Instructions:**
Round to the nearest tenth of a percent.
**Input Section:**
A blank text box is provided for input, followed by an "Enter" button to submit the response.
### Graphs and Diagrams:
There are no graphs or diagrams in this assignment; it is purely a textual problem dealing with a binomial experiment.
To find the requested probability, you would typically use the binomial probability formula or a cumulative binomial probability table:
\[ P(X \leq k) = \sum_{i=0}^{k} \binom{n}{i} p^i (1-p)^{n-i} \]
where:
- \( \binom{n}{i} \) is the binomial coefficient
- \( X \) is the random variable representing the number of successes
- \( k \) is the maximum number of successes (which is 2 in this problem)
By applying the values into the formula, you can calculate the required probability.
**Remember:** This is a critical concept in the study of probability and statistics, particularly useful in understanding experimental outcomes and their likelihoods.
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