An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Define events: A (no 4-wheel drive), B (third-row seats).
Find the number of cars with no 4-wheel drive and third-row seats: 12.
Find the total number of cars with no 4-wheel drive: 40.
Calculate the conditional probability: P ( B ∣ A ) = 40 12 = 0.3 .
Explanation
Understand 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 Let A be the event that a randomly selected car has no 4-wheel drive. Let B be the event that a randomly selected car has third-row seats. We want to find P(B|A), the probability that a car has third-row seats given that it has no 4-wheel drive.
State the formula The conditional probability formula is given by: P ( B ∣ A ) = P ( A ) P ( A ∩ B ) In this case, we can find the probabilities directly from the table.
Find the values from the table From the table, the number of cars with no 4-wheel drive and third-row seats is 12. The number of cars with no 4-wheel drive is 40. Therefore, the probability that a randomly selected car with no 4-wheel drive has third-row seats is: P ( B ∣ A ) = 40 12
Simplify the fraction Now, we simplify the fraction: 40 12 = 20 6 = 10 3 = 0.3
State the final answer Therefore, the probability that a randomly selected car with no 4-wheel drive has third-row seats is 0.3.
Examples
This type of probability calculation is used in market research to understand customer preferences. For example, a car company might want to know the probability that a customer who prefers a car with no 4-wheel drive also wants third-row seats. This information can help the company tailor its marketing efforts and product offerings to better meet customer needs. Understanding these probabilities allows for more effective targeting and resource allocation in marketing campaigns.
