Homework Help is Here – Start Your Trial Now!
Math
Statistics
10 (")( 210 4 1024 %3D 1/2 10

10 (")( 210 4 1024 %3D 1/2 10

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

is there any way you can figure out how to get that answer (210/1024)?  

The expression given is: \[ \left( \binom{10}{4} \right) \left( \frac{1}{2} \right)^{10} = \frac{210}{1024} \] **Explanation:** 1. **Binomial Coefficient**: \(\binom{10}{4}\) represents the binomial coefficient, which is the number of ways to choose 4 elements from a set of 10 elements without regard to order. It is calculated as: \[ \binom{10}{4} = \frac{10!}{4!(10-4)!} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 210 \] 2. **Fraction**: \(\left(\frac{1}{2}\right)^{10}\) denotes raising the fraction \(\frac{1}{2}\) to the 10th power, which means: \[ \left(\frac{1}{2}\right)^{10} = \frac{1}{1024} \] 3. **Equation**: The left side of the equation combines these two components: \[ 210 \times \frac{1}{1024} = \frac{210}{1024} \] This equation illustrates a binomial probability scenario, where the probability of a specific outcome (occurring 4 times in 10 trials) with a probability of \(\frac{1}{2}\) per trial is calculated.
Transcribed Image Text:The expression given is: \[ \left( \binom{10}{4} \right) \left( \frac{1}{2} \right)^{10} = \frac{210}{1024} \] **Explanation:** 1. **Binomial Coefficient**: \(\binom{10}{4}\) represents the binomial coefficient, which is the number of ways to choose 4 elements from a set of 10 elements without regard to order. It is calculated as: \[ \binom{10}{4} = \frac{10!}{4!(10-4)!} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 210 \] 2. **Fraction**: \(\left(\frac{1}{2}\right)^{10}\) denotes raising the fraction \(\frac{1}{2}\) to the 10th power, which means: \[ \left(\frac{1}{2}\right)^{10} = \frac{1}{1024} \] 3. **Equation**: The left side of the equation combines these two components: \[ 210 \times \frac{1}{1024} = \frac{210}{1024} \] This equation illustrates a binomial probability scenario, where the probability of a specific outcome (occurring 4 times in 10 trials) with a probability of \(\frac{1}{2}\) per trial is calculated.
Expert Solution
Step 1

 

 

 

steps

Step by step

Solved in 2 steps with 10 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Fundamental Counting Principle
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS