- Identify the total count of cars with "No 4-Wheel Drive", which is 40.
- Identify the subset of these cars that have "Third-Row Seats", which is 12.
- Calculate the conditional probability as the ratio of these two values: \(\frac{12}{40}\).
- Simplify the fraction to find the final result: \(\boxed{0.3}\).
Explanation
- Analyze the provided data
We are given a two-way table representing the inventory of SUVs at a car lot. To determine the probability that a randomly selected car with 'No 4-Wheel Drive' also has 'Third-Row Seats', we must focus only on the subset of cars that satisfy the condition 'No 4-Wheel Drive'.
- Identify the relevant groups within the table
From the table, we look at the column labeled 'No 4-Wheel Drive'. The total number of cars in this category is the sum of those with and without third-row seats, which is given as 40. Within this specific group of 40 cars, we identify the number of cars that have third-row seats, which is 12.
- Calculate the conditional probability
The probability of an event occurring given a certain condition is calculated by dividing the number of favorable outcomes (cars with both 'No 4-Wheel Drive' and 'Third-Row Seats') by the total number of outcomes that satisfy the condition (all cars with 'No 4-Wheel Drive'). Thus, the probability \(P\) is:
\[P = \frac{\text{Number of cars with No 4WD and Third-Row Seats}}{\text{Total number of cars with No 4WD}} = \frac{12}{40}\]
- Simplify the result and conclude
Now, we simplify the fraction \(\frac{12}{40}\) to its simplest form. Dividing both the numerator and the denominator by their greatest common divisor, which is 4, we get:
\[\frac{12 \div 4}{40 \div 4} = \frac{3}{10} = 0.3\]
Thus, the probability is 0.3.
Examples
This type of problem helps in market research and inventory management. For instance, if a dealership wants to know the likelihood that a customer requesting a car without 4-wheel drive will also want third-row seating, they can use this conditional probability to optimize their stock levels. By analyzing \(\frac{12}{40} = 0.3\), the manager knows that 30% of their "No 4-Wheel Drive" inventory meets this specific requirement.