To calculate the probability of a specific number of successes in a binomial distribution, we can use the binomial probability formula:

$P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}$

Where:

• $P(X = k)$ is the probability of getting exactly $k$ successes.
• $\binom{n}{k}$ is the binomial coefficient, which is calculated as $\frac{n!}{k!(n - k)!}$.
• $n$ is the number of trials.
• $k$ is the number of successes.
• $p$ is the probability of success on a single trial.
• $1 - p$ is the probability of failure.

Given:

• The probability of success $p = \frac{11}{60}$,
• The number of trials $n$, and
• The desired number of successes $k$, which you should specify.

If you provide the number of trials ($n$) and the number of successes ($k$), I can compute the probability.

Would you like to provide those values or clarify any details?

Follow-up questions:

1. What is the exact number of trials ($n$) for your binomial experiment?
2. How many successes ($k$) are you interested in calculating the probability for?
3. Are you familiar with using the binomial probability formula, or would you prefer assistance with that?
4. Would you like guidance on calculating the probability using Excel or another tool?
5. Are you working with a specific application of this binomial distribution (e.g., real-world data)?

Tip: For small values of $n$, manual computation using the binomial formula is feasible, but for larger values, tools like Excel or software like Python can significantly speed up the process!