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The problem presented involves a **binomial distribution**, where the number of trials \(n = 11\) and the probability of success in each trial \(p = 0.37\). The question asks for the probability that the experiment results in more than 1 success.

To solve this, we will compute the cumulative probability for having **1 or fewer successes** and then subtract that from 1 to find the probability of having **more than 1 success**.

### Steps to Solve:

1. **Binomial Formula**:
   The probability of getting exactly \(k\) successes in \(n\) independent trials is given by the binomial probability formula:
   \[
   P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
   \]
   Where:
   - \( \binom{n}{k} \) is the binomial coefficient, calculated as \( \frac{n!}{k!(n-k)!} \).
   - \(p = 0.37\) is the probability of success.
   - \(1 - p = 0.63\) is the probability of failure.

2. **Cumulative Probability for \(X \leq 1\)**:
   We will calculate the probabilities for \(X = 0\) and \(X = 1\), then sum them up.
   - For \(X = 0\):
     \[
     P(X = 0) = \binom{11}{0} (0.37)^0 (0.63)^{11} = (1)(1)(0.63^{11})
     \]
   - For \(X = 1\):
     \[
     P(X = 1) = \binom{11}{1} (0.37)^1 (0.63)^{10} = (11)(0.37)(0.63^{10})
     \]
   
3. **Probability of More than 1 Success**:
   Once we compute \(P(X = 0)\) and \(P(X = 1)\), we subtract their sum from 1:
   \[
   P(X > 1) = 1 - (P(X = 0) + P(X = 1))
   \]

I will compute the values based on these formulas.

### Computation:

- \(P(X = 0) = 0.06344\)
- \(P(X = 1) = 0.18844\)

Now, summing those:
\[
P(X \leq 1) = P(X = 0) + P(X = 1) = 0.06344 + 0.18844 = 0.25188
\]

Finally, the probability of more than 1 success:
\[
P(X > 1) = 1 - 0.25188 = 0.74812
\]

### Final Answer:
The probability that the experiment results in more than 1 success is approximately **0.748**.

Would you like more details on any of the steps or further clarifications?

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**Related Questions**:
1. How would the probability change if the probability of success \(p\) was higher?
2. What is the probability of getting exactly 5 successes in this scenario?
3. How does the binomial distribution compare to a normal distribution for large \(n\)?
4. How can we generalize the binomial formula for different values of \(k\)?
5. What is the mean and standard deviation of this binomial distribution?

**Tip**: Always check if a binomial distribution can be approximated by a normal distribution when the number of trials \(n\) is large!

A binomial experiment with probability of success p = 0.37 and n = 11 trials is conducted. What is the probability that the experiment results in more than 1 success?

Learn how to calculate the probability of more than 1 success in a binomial experiment with 11 trials and a success probability of 0.37. Explore the use of binomial distribution, the cumulative distribution function, and step-by-step calculations.

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