To find the experimental probability that the next muffin sold will be a pumpkin spice muffin, we first need to determine the total number of muffins sold.
The total number of muffins sold is the sum of all the muffins:
\[ 3 \text{ (pumpkin spice)} + 4 \text{ (blueberry)} + 4 \text{ (bran)} + 7 \text{ (blackberry)} = 18 \text{ muffins} \]
Now, the probability of selling a pumpkin spice muffin is given by the formula:
\[ P(\text{pumpkin spice muffin}) = \frac{\text{Number of pumpkin spice muffins sold}}{\text{Total number of muffins sold}} \]
Substituting the values we have:
\[ P(\text{pumpkin spice muffin}) = \frac{3}{18} \]
Next, we simplify the fraction:
\[ \frac{3}{18} = \frac{1}{6} \]
So, the experimental probability that the next muffin sold will be a pumpkin spice muffin is:
\[ P(\text{pumpkin spice muffin}) = \frac{1}{6} \]