Customer Purchases at a Gas Station
| Beverage purchased | Beverage not purchased | Total | |
|---|---|---|---|
| Gasoline purchased | 60 | 25 | 85 |
| Gasoline not purchased | 35 | 15 | 50 |
| Total | 95 | 40 | 135 |
On Tuesday, a local gas station had 135 customers. The table above summarizes whether the customers purchased gasoline and/or a beverage. Based on the data, what is the probability that a randomly selected customer that day did not purchase gasoline?
For two-way table probability questions, first translate the wording carefully into "favorable outcomes" and "total outcomes." If the question says "a randomly selected customer" with no "given that" condition, use the grand total from the table as the denominator. Then identify all cells that match the described event (for example, all customers who did not purchase gasoline, regardless of other behavior), add those counts for the numerator, and form the probability fraction. Always double-check whether the problem is asking for an unconditional probability (use total) or a conditional probability (use the relevant row or column total).
Hints
Recall the basic probability formula
Probability is usually found by dividing the number of favorable outcomes by the total number of possible outcomes. What are the "favorable" outcomes here?
Locate the correct cells in the table
Focus on the row "Gasoline not purchased." How many customers are in that row altogether, regardless of beverage purchase?
Choose the correct denominator
Are we choosing from all 135 customers, or only from a subset like those who bought or did not buy beverages or gasoline? Use the total group the random choice is coming from as the denominator.
Desmos Guide
Compute the desired probability as a fraction
In Desmos, type (35+15)/135 and press Enter. This expression represents (number who did not purchase gasoline) divided by (total customers), and Desmos will show its value as a decimal and/or simplified fraction.
Compare with each answer choice
Type each answer choice into Desmos: 15/50, 15/40, 35/50, and 50/135. Compare their decimal values or fractions to the value you got from (35+15)/135; the matching one corresponds to the correct option.
Step-by-step Explanation
Identify what probability is being asked
The question says "a randomly selected customer" and asks for the probability that this customer did not purchase gasoline.
This means we want:
- Favorable outcomes: all customers who did not purchase gasoline.
- Total outcomes: all 135 customers that day.
Count customers who did not purchase gasoline
Look at the row labeled "Gasoline not purchased."
- Beverage purchased and gasoline not purchased: 35 customers.
- Beverage not purchased and gasoline not purchased: 15 customers.
Add these to get the total number of customers who did not purchase gasoline:
35 + 15 = 50.
Use the total number of customers for the denominator
Because the customer is chosen randomly from all customers that day, the denominator of the probability fraction is the total number of customers.
From the table, the total number of customers is 135 (bottom-right corner).
Write the probability as a fraction and match the answer choice
Probability is given by
- Probability (number who did not purchase gasoline) / (total number of customers).
So the probability is .
Among the answer choices, this is choice D) 50/135.