10 (")( 210 4 1024 %3D 1/2 10
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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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafd73554-b37d-4080-8e8c-85a6082f7e6c%2Fd629baea-f0b7-47ae-a12d-cd1f9328482e%2Fi47gcek_processed.jpeg&w=3840&q=75)
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.
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