An automobile manufacturer produces $50 \%$ of its cars at plant A. If $3 \%$ of the cars manufactured at plant A have defective emissions control devices, what is the probability that one of this manufacturer's cars was manufactured at plant A and has a defective emissions control device?
Probability $=\square$ (Type an integer or decimal.)
Answer
Final Answer: The probability that one of this manufacturer's cars was manufactured at plant A and has a defective emissions control device is \(\boxed{0.015}\) or \(\boxed{1.5\%}\).
Step 1 ：The problem is asking for the probability that a car was both manufactured at plant A and has a defective emissions control device. This is a conditional probability problem.
Step 2 ：We know that 50% of the cars are manufactured at plant A, and among those, 3% have defective emissions control devices.
Step 3 ：So, the probability that a car was both manufactured at plant A and has a defective emissions control device is simply the product of these two probabilities.
Step 4 ：Let's denote the probability of a car being manufactured at plant A as \(probability_A = 0.5\) and the probability of a car having a defective device given it was manufactured at plant A as \(probability_defective_given_A = 0.03\).
Step 5 ：The probability that a car was both manufactured at plant A and has a defective emissions control device is \(probability_A\) times \(probability_defective_given_A\), which equals to \(0.5 * 0.03 = 0.015\).
Step 6 ：Final Answer: The probability that one of this manufacturer's cars was manufactured at plant A and has a defective emissions control device is \(\boxed{0.015}\) or \(\boxed{1.5\%}\).
