Find the probability of exactly 5 Mexican-Americans among 12 jurors. Round your answer to four decimal places.

To find the probability of exactly 5 Mexican-Americans among 12 jurors, we can use the **binomial probability formula**. The formula is:

\[
P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}
\]

Where:
- \( n \) is the total number of trials (jurors), which is 12.
- \( k \) is the number of successes (Mexican-Americans), which is 5.
- \( p \) is the probability of success on a single trial.
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \(\frac{n!}{k!(n-k)!}\).

If the probability \( p \) of a juror being Mexican-American is known, we can plug in the values to compute the probability. If \( p \) is not provided, it's typically assumed or estimated based on the context.

Please provide the value of \( p \), or if it is not given, I can proceed with an assumption (e.g., using the proportion of Mexican-Americans in the population if that’s appropriate).

Learn how to calculate the binomial probability of selecting exactly 5 Mexican-Americans among 12 jurors using the binomial distribution formula. This problem involves key concepts in probability, including the binomial probability formula and the binomial theorem. Suitable for high school students in Grades 10-12.

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