Questions: Names: Student Learning Outcomes - The student will use theoretical and empirical methods to estimate probabilities. - The student will appraise the differences between the two estimates. - The student will demonstrate an understanding of long-term relative frequencies. Do the Experiment Count out 40 mixed-color MMs which is approximately one small bag's worth. Record the number of each color in Table 3.11. Use the information from this table to complete Table 3.12. Leave your answers in unreduced fractional form. Do not multiply out any fractions. Color Yellow (n) Green (G) Blue (BL) Brown (B) Orange (O) Red (R) Table 3.11 Population Quantity

Solution Steps

Add up the quantities of each color to find the total number of M&Ms.

\[ 10 + 7 + 8 + 16 + 6 + 3 = 50 \]

Divide the quantity of each color by the total number of M&Ms to find the probability of each color.

• Yellow (Y): \(\frac{10}{50} = \frac{1}{5}\)
• Green (G): \(\frac{7}{50}\)
• Blue (BL): \(\frac{8}{50} = \frac{4}{25}\)
• Brown (B): \(\frac{16}{50} = \frac{8}{25}\)
• Orange (O): \(\frac{6}{50} = \frac{3}{25}\)
• Red (R): \(\frac{3}{50}\)

Ensure that the sum of all probabilities equals 1.

\[ \frac{1}{5} + \frac{7}{50} + \frac{4}{25} + \frac{8}{25} + \frac{3}{25} + \frac{3}{50} \]

Convert all fractions to a common denominator (50):

\[ \frac{10}{50} + \frac{7}{50} + \frac{8}{50} + \frac{16}{50} + \frac{6}{50} + \frac{3}{50} = \frac{50}{50} = 1 \]

Final Answer