To find the probability that a randomly chosen customer purchased french fries and a deli sandwich, we need to identify the relevant numbers and then use the probability formula.
1. Identify total number of combo purchases:
We sum up all the purchases from the entire table, which includes hamburgers, pizzas, and deli sandwiches, combined with french fries, peanuts, and popcorn.
[tex]\[
\begin{align*}
\text{Total purchases} & = \text{French Fries with Hamburger} + \text{French Fries with Pizza} + \text{French Fries with Deli Sandwich} \\
& + \text{Peanuts with Hamburger} + \text{Peanuts with Pizza} + \text{Peanuts with Deli Sandwich} \\
& + \text{Popcorn with Hamburger} + \text{Popcorn with Pizza} + \text{Popcorn with Deli Sandwich} \\
& = 83 + 67 + 37 \\
& + 2 + 5 + 14 \\
& + 19 + 29 + 3 \\
& = 259
\end{align*}
\][/tex]
2. Identify the number of times french fries and a deli sandwich were purchased together:
The given value for french fries and deli sandwich purchases is [tex]\( 37 \)[/tex].
3. Calculate the probability:
The probability [tex]\( P \)[/tex] can be calculated using the ratio of the number of favorable outcomes (purchases of french fries and deli sandwiches) to the total number of outcomes (all purchases).
[tex]\[
P(\text{French Fries and Deli Sandwich}) = \frac{\text{Number of French Fries and Deli Sandwich purchases}}{\text{Total number of purchases}}
\][/tex]
Substituting the values:
[tex]\[
P(\text{French Fries and Deli Sandwich}) = \frac{37}{259}
\][/tex]
This fraction is already in its simplest form.
Hence, the probability that a randomly chosen customer purchased french fries and a deli sandwich is:
[tex]\[
\boxed{\frac{37}{259}}
\][/tex]
