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Answer :
The probability that one of this manufacturer's cars was manufactured at plant A and has a defective emissions control device is 0.0408, or 4.08%
To find the probability that one of the manufacturer's cars was manufactured at plant A and has a defective emissions control device, we need to calculate the joint probability of these two events occurring.
First, we know that 68% of the cars are manufactured at plant A. This means that the probability of a car being manufactured at plant A is 0.68.
Next, we know that 6% of the cars manufactured at plant A have defective emissions control devices. This means that the probability of a car from plant A having a defective emissions control device is 0.06.
To find the joint probability, we multiply the individual probabilities together.
Probability of a car being manufactured at plant A and having a defective emissions control device = Probability of being manufactured at plant A * Probability of having a defective emissions control device
= 0.68 * 0.06
= 0.0408
Therefore, the probability that one of this manufacturer's cars was manufactured at plant A and has a defective emissions control device is 0.0408, or 4.08%.
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