The two-way table shows the number of sport utility vehicles with certain features for sale at the car lot.
| | 4-Wheel Drive | No 4-Wheel Drive | Total |
| :----------------- | :------------ | :--------------- | :---- |
| Third-Row Seats | 18 | 12 | 30 |
| No Third-Row Seats | 7 | 28 | 35 |
| Total | 25 | 40 | 65 |
What is the probability that a randomly selected car with no 4-wheel drive has third-row seats?
A. 0.8
B. 0.7
C. 0.4
D. 0.3
Answer (2)
Define events A (no 4-wheel drive) and B (third-row seats).
Find the probability P(A and B) = 65 12 .
Find the probability P(A) = 65 40 .
Calculate the conditional probability P(B|A) = P ( A ) P ( A and B ) = 40/65 12/65 = 0.3 .
Explanation
Analyze the problem Let's analyze the problem. We are given a two-way table that shows the number of sport utility vehicles with certain features for sale at a car lot. The features are 4-wheel drive and third-row seats. We want to find the probability that a randomly selected car with no 4-wheel drive has third-row seats.
Define events and conditional probability Let A be the event that a randomly selected car has no 4-wheel drive, and let B be the event that a randomly selected car has third-row seats. We want to find the conditional probability P(B|A), which is the probability that a car has third-row seats given that it has no 4-wheel drive. The formula for conditional probability is P(B|A) = P(A and B) / P(A).
Find P(A and B) and P(A) From the table, the number of cars with no 4-wheel drive and third-row seats is 12. The total number of cars is 65. So, P(A and B) = 12/65. From the table, the number of cars with no 4-wheel drive is 40. So, P(A) = 40/65.
Calculate P(B|A) Therefore, P(B|A) = (12/65) / (40/65) = 12/40 = 3/10 = 0.3.
Examples
This type of probability calculation is useful in market research. For example, if a car dealer wants to know the likelihood that a customer looking for a car without 4-wheel drive also wants third-row seats, they can use this calculation to understand customer preferences and tailor their marketing strategies accordingly. Knowing this probability helps the dealer stock the right mix of vehicles to meet customer demand.
The probability that a randomly selected car with no 4-wheel drive has third-row seats is 0.3, which is calculated by determining the number of cars fitting both criteria divided by the total number of cars with no 4-wheel drive. Therefore, the correct answer is option D. 0.3.
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