Sure, I'd be happy to walk you through the detailed, step-by-step solution for finding the experimental probability of a randomly chosen food item tasting sweet based on the provided table of flavor frequencies.
The table given is:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Flavor} & \text{Frequency} \\
\hline \text{salty} & 8 \\
\hline \text{sweet} & 3 \\
\hline \text{spicy} & 5 \\
\hline \text{sour} & 9 \\
\hline
\end{array}
\][/tex]
### Step-by-Step Solution:
1. Identify the total number of food items sampled:
To find the total number of food items, we sum the frequencies of each flavor.
[tex]\[
\text{Total items} = 8 + 3 + 5 + 9 = 25
\][/tex]
2. Identify the number of sweet tasting items:
The number of food items that taste sweet is given directly in the table.
[tex]\[
\text{Sweet items} = 3
\][/tex]
3. Calculate the experimental probability:
The experimental probability is the ratio of the number of sweet tasting items to the total number of food items.
[tex]\[
\text{Experimental Probability (Sweet)} = \frac{\text{Sweet items}}{\text{Total items}} = \frac{3}{25}
\][/tex]
### Conclusion:
So, the experimental probability of a randomly chosen food item tasting sweet is [tex]\(\frac{3}{25}\)[/tex].
This matches the first option in the given choices:
[tex]\[
\frac{3}{25}
\][/tex]
