Questions: QUESTION 11 , 1 POINT A college algebra class has 28 enrolled students. Of those, 4 are taking this course a second time. The class professor wants to test the effectiveness of an online game designed to help students learn algebra operations. She randomly divides the class into two equal group - a test group who will play the game and a control group who will not play the game. Find the probability that 3 of the students selected for the test group are among those taking the course a second time. Use a TI-83, TI- 83 plus, or TI- 84 calculator to find the probability. - Round your answer to three decimal places. Provide your answer below:

△ Find the probability that 3 of the students selected for the test group are among those taking the course a second time. ○ Identify total students and repeat students ☼ Total students = 28, students taking the course a second time = 4. ○ Divide class into groups ☼ Number of students in each group = 28 / 2 = 14. ○ Set up hypergeometric distribution ☼ Let \( N = 28 \), \( K = 4 \), \( n = 14 \), \( k = 3 \). We use the hypergeometric distribution: \( P(X=k) = \frac{C(K, k) \times C(N-K, n-k)}{C(N, n)} \). ○ Calculate binomial coefficients ☼ \( C(4, 3) = 4 \), \( C(24, 11) = 2,496,144 \), \( C(28, 14) = 40,116,600 \). ○ Substitute into hypergeometric formula ☼ \( P(X=3) = \frac{4 \times 2,496,144}{40,116,600} = \frac{9,984,576}{40,116,600} \). ○ Calculate probability ☼ The probability is approximately 0.249. ✧ The probability is 0.249. ☺0.249