Answer:
To calculate the probability, you 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 (students chosen),
- \( k \) is the number of successful trials (female students chosen),
- \( \binom{n}{k} \) is the number of ways to choose \( k \) successes out of \( n \) trials,
- \( p \) is the probability of success (probability of choosing a female student),
- \( 1 - p \) is the probability of failure (probability of choosing a male student).
In this case:
- \( n = 5 \) (5 students chosen),
- \( k = 3 \) (3 female students chosen),
- \( p \) is the probability of choosing a female student, which is \( \frac{4}{11} \) (since there are 4 female students out of 11).
Now, plug these values into the formula:
\[ P(X = 3) = \binom{5}{3} \cdot \left(\frac{4}{11}\right)^3 \cdot \left(\frac{7}{11}\right)^2 \]
Calculate \( \binom{5}{3} \) (which is 10), then perform the calculations:
\[ P(X = 3) = 10 \cdot \left(\frac{4}{11}\right)^3 \cdot \left(\frac{7}{11}\right)^2 \]
Now, round your answer to 3 decimal places.