# 1. Introduction

This R program demonstrates how to fit a Binomial distribution to a given set of data. The Binomial distribution is a common probability distribution that describes the number of successes in a fixed number of trials in an experiment.

# 2. Program Steps

1. Create a sample dataset representing the number of successes in trials.

2. Fit a Binomial distribution to the data.

3. Estimate the probability of success.

4. Print the estimated probability.

# 3. Code Program

``````# Step 1: Create a sample dataset
data <- rbinom(100, size = 10, prob = 0.5)  # Generating binomial data for illustration

# Step 2: Fit a Binomial distribution to the data
# Estimate the probability of success
size <- 10  # Number of trials
prob_estimate <- mean(data) / size

# Step 3: Print the estimated probability
print("Estimated probability of success:")
print(prob_estimate)

# Note: The actual probability used in rbinom is for demonstration purposes and typically unknown in real-world scenarios. This step is estimating it from the data.

``````

### Output:

```Estimated probability of success:
[Estimated Probability Value]
```

### Explanation:

1. rbinom(100, size = 10, prob = 0.5): Generates 100 data points following a Binomial distribution with size = 10 trials and prob = 0.5 probability of success.

2. mean(data) / size: Calculates the mean of the data and divides by the number of trials to estimate the probability of success.

3. print("Estimated probability of success:"), print(prob_estimate): Prints the estimated probability of success in the Binomial distribution.