Question

a bakery recorded how many muffins it recently sold. type of muffin number sold blueberry 16 chocolate chip 21 cinnamon 13 banana nut 8 based on this data, what is the probability that the next muffin sold will be a cinnamon muffin? \\(\frac{13}{45}\\) \\(\frac{1}{13}\\) \\(\frac{13}{58}\\) \\(\frac{13}{100}\\)

Explanation:

Step1: Calculate total muffins sold

Sum the number of each type of muffin sold: \(16 + 21 + 13 + 8\)
\(16+21 = 37\), \(37+13 = 50\), \(50+8 = 58\)? Wait, no, 16+21 is 37, 37+13 is 50, 50+8 is 58? Wait, no, 16+21=37, 37+13=50, 50+8=58? Wait, no, 16+21=37, 37+13=50, 50+8=58? Wait, no, let's recalculate: 16 (blueberry) + 21 (chocolate chip) = 37; 37 + 13 (cinnamon) = 50; 50 + 8 (banana nut) = 58? Wait, no, 16+21=37, 37+13=50, 50+8=58? Wait, no, 16+21=37, 37+13=50, 50+8=58? Wait, maybe I made a mistake. Wait, 16+21=37, 37+13=50, 50+8=58? Wait, no, 16+21=37, 37+13=50, 50+8=58? Wait, no, 16+21=37, 37+13=50, 50+8=58? Wait, maybe the total is 16+21+13+8 = 58? Wait, but the first option is 13/45, second 1/13, third 13/58, fourth 13/100. Wait, let's recalculate the total: 16 (blueberry) + 21 (chocolate chip) = 37; 37 + 13 (cinnamon) = 50; 50 + 8 (banana nut) = 58. So total muffins sold is 58. The number of cinnamon muffins sold is 13. So the probability is the number of cinnamon muffins divided by total muffins, which is \( \frac{13}{58} \)? Wait, but wait, 16+21=37, 37+13=50, 50+8=58? Wait, 16+21=37, 37+13=50, 50+8=58. Yes. So the probability is 13/58. Wait, but let's check again: 16 (blueberry) +21 (chocolate chip)=37; 37+13 (cinnamon)=50; 50+8 (banana nut)=58. So total is 58. So the probability of selling a cinnamon muffin is number of cinnamon muffins (13) divided by total (58), so \( \frac{13}{58} \).

Step2: Determine the probability

Probability formula: \( P(\text{cinnamon}) = \frac{\text{Number of cinnamon muffins sold}}{\text{Total number of muffins sold}} \)
Number of cinnamon muffins sold = 13, Total number of muffins sold = 16 + 21 + 13 + 8 = 58.
So \( P(\text{cinnamon}) = \frac{13}{58} \)

Answer:

\(\frac{13}{58}\) (corresponding to the option with \(\frac{13}{58}\))