To determine the probability that the next customer will pay with a debit card, we first need to find the total number of customers and the number of customers who used a debit card.
From the data provided:
- Cash customers: 65
- Debit card customers: 2
- Credit card customers: 9
Now, we can calculate the total number of customers:
\[ \text{Total customers} = 65 + 2 + 9 = 76 \]
Next, we know that the number of customers who paid with a debit card is 2. The probability \( P \) of the next customer paying with a debit card is given by the ratio of the number of debit card customers to the total number of customers:
\[ P(\text{debit card}) = \frac{\text{Number of debit card customers}}{\text{Total customers}} = \frac{2}{76} \]
Now, we simplify the fraction \( \frac{2}{76} \):
\[ \frac{2 \div 2}{76 \div 2} = \frac{1}{38} \]
Thus, the probability that the next customer will pay with a debit card, expressed as a fraction in simplest form, is
\[ \boxed{\frac{1}{38}} \]