Step 5 Step 4Using the values we have previously determined, \( N = 13 \), \( M = 7 \), \( n = 6 \), and \( k = 5 \). The remaining values needed for the formula are \( N - M \) and \( n - k \).Find \( N - M \).\[ N - M = 13 - 7 \]\[ = 6 \]Find \( n - k \).\[ n - k = 6 - 5 \]\[ = 1 \]---Step 5Refer to these values from the previous step.\[ N = 13, M = 7, n = 6, k = 5, N - M = 6, n - k = 1 \]Substitute these values into the hypergeometric probability formula, or use technology. Round your answer to four decimal places.\[ P(x = k) = \frac{\binom{M}{k} \binom{N-M}{n-k}}{\binom{N}{n}} \]\[ P(x = 5) = \frac{\binom{7}{5} \binom{6}{1}}{\binom{13}{6}} \]\[ = \]Therefore, the probability of selecting five brown and one red M&Ms from a candy dish containing seven brown and six red M&Ms is \(\boxed{}\). **Tutorial Exercise: Hypergeometric Distribution****Scenario:**A candy dish contains seven brown and six red M&Ms. A child selects six M&Ms without checking the colors. What is the probability that there are five brown and one red M&M in the selection?**Step 1: Determine the Appropriateness of the Hypergeometric Distribution**- Begin by confirming that the hypergeometric distribution is appropriate for this sample.- The proportion, \( \frac{n}{N} = \frac{6}{13} \). Calculate this value:\[\frac{n}{N} = 0.46\]- Check if \( \frac{n}{N} \geq 0.05 \), where \( n = 6 \) (the number of M&Ms being selected), and \( N = 13 \) (the total number of M&Ms).- Since 0.46 is greater than 0.05, we can use the hypergeometric probability distribution.**Step 2: Define Variables for the Hypergeometric Distribution**- Recall that for a hypergeometric distribution, the population contains \( M \) successes and \( N - M \) failures.- Brown M&M is considered a success, red M&M a failure.- Given seven brown and six red M&Ms, the total number of M&Ms is \( N = 13 \) and successes (brown M&Ms) \( M = 7 \).**Step 3: Calculate the Probability**- Use the formula for the probability of exactly \( k \) successes in a sample of size \( n \):\[P(x = k) = \frac{C_k^M C_{n-k}^{N-M}}{C_n^N}\]- With seven brown M&Ms in a bowl of thirteen, \( M = 7 \), \( N = 13 \).- For a sample size \( n = 6 \): - \( k = 5 \) (number of successes or brown M&Ms).- We are calculating the probability of exactly five brown M&Ms when six are drawn.

Answered: Image /qna-images/answer/5d2e925e-aefd-4639-b1e1-ad3221bee05f.jpg

Refer to these values from the previous step. N = 13, M = 7, n = 6, k = 5, NM = 6, n - k = 1 Substitute these values into the hypergeometric probability formula, or use technology. Round your answer to four decimal places. CMC-k N-M P(x = k) = P(x = 5) = c57C₁6 13 N Therefore, the probability of selecting five brown and one red M&Ms from a candy dish containing seven brown and six red M&Ms is