Sure, let's break this down step-by-step to find the probability that a randomly selected car with no 4-wheel drive has third-row seats.
1. Understand the Problem:
We are given a two-way table that shows the number of sport utility vehicles with certain features (4-wheel drive and third-row seats) available at a car lot. We need to find the probability that a car selected randomly from those without 4-wheel drive has third-row seats.
2. Identify Relevant Data:
- Total number of cars without 4-wheel drive: 40
- Number of cars without 4-wheel drive that have third-row seats: 12
3. Set Up the Probability Formula:
The probability [tex]\( P \)[/tex] of an event is given by:
[tex]\[
P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
4. Apply the Numbers:
In this case, the event is selecting a car with no 4-wheel drive that has third-row seats. Therefore:
[tex]\[
P(\text{Third-row seats | No 4-wheel drive}) = \frac{\text{Number of cars with no 4-wheel drive that have third-row seats}}{\text{Total number of cars with no 4-wheel drive}}
\][/tex]
Plugging in the numbers:
[tex]\[
P(\text{Third-row seats | No 4-wheel drive}) = \frac{12}{40}
\][/tex]
5. Simplify the Fraction:
Simplify [tex]\(\frac{12}{40}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD):
[tex]\[
\frac{12}{40} = \frac{12 \div 4}{40 \div 4} = \frac{3}{10}
\][/tex]
6. Convert to Decimal:
[tex]\(\frac{3}{10}\)[/tex] as a decimal is 0.3.
So, the probability that a randomly selected car with no 4-wheel drive has third-row seats is [tex]\( \boxed{0.3} \)[/tex].
