# Probability using binomial distribution

• megr_ftw
However, it is also possible for there to be 0 errors (if no errors occur) or 2 errors (if two errors occur and one is not able to be corrected).
megr_ftw

## Homework Statement

In a comm. system a byte (8 bits) is transmitted with a bit error probability of 0.1. If the system can correct at most one error made in each byte.
a) what is probability of a byte being received correctly (after correction)?
b)What is most probable number of errors (after correction) in a byte

binomial tables?

## The Attempt at a Solution

im sure this is a binomial distribution and need to use the equation for it an for part a) i got 0.19 and I am not sure it that's right. But part b) is confusing me so I wanted to make sure part a) was correct..

Your solution for part a) is incorrect. The probability of a byte being received correctly (after correction) should be 0.9, as this is the probability of no bit errors occurring in the transmission. This can be calculated using the binomial distribution formula.

For part b), the most probable number of errors (after correction) in a byte would be 1, as the system can only correct at most one error in each byte. This means that if an error occurs, it will most likely be corrected, resulting in only one error in the byte.

## 1. What is the binomial distribution and when is it used?

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials. It is used when there are two possible outcomes (success or failure) in each trial and the probability of success remains constant throughout the trials.

## 2. How is the binomial distribution different from other probability distributions?

The binomial distribution differs from other probability distributions in that it only considers two possible outcomes, while other distributions may have more than two outcomes. Additionally, the binomial distribution assumes that each trial is independent and the probability of success remains constant.

## 3. What are the key features of the binomial distribution?

The key features of the binomial distribution include the number of trials (n), the probability of success in each trial (p), and the number of successes (x). These features are used to calculate the probability of a specific number of successes occurring in a given number of trials.

## 4. How is the binomial distribution used in real-world applications?

The binomial distribution is commonly used in real-world applications such as market research, quality control, and medical trials. It can also be used to model phenomena such as coin flips, election outcomes, and sports statistics.

## 5. What is the formula for calculating the probability using binomial distribution?

The formula for calculating the probability using binomial distribution is P(x) = (nCx)(p^x)(q^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (1-p).

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