Question

The Breaker's Manufacturing Company makes 80% of a particular sensor, the Cartin Company makes 15% of them, and the Flutes Company makes the other 5%. The sensors made by Breaker's have a 4% defect rate, the Cartin sensors have a 6% defect rate, and the Flutes sensors have a 9% defect rate. If a sensor is randomly selected from the general population of all sensors, what is the probability that it is defective, given that it was made by Cartin Company? A. 0.04 B. 0.05 C. 0.06 D. 0.15

Answer 1

Option C: 0.06 is the correct answer.

Step-by-step explanation:

Given information is:

The Breaker's Manufacturing Company makes 80% of a particular sensor, the Cartin Company makes 15% of them, and the Flutes Company makes the other 5%.

The sensors made by Breaker's have a 4% defect rate, the Cartin sensors have a 6% defect rate, and the Flutes sensors have a 9% defect rate.

The defect rate of any company is equal to the probability of a randomly selected sensor from that company being defective.

Cartin's sensors have a 6% defect rate, so, the probability that it is defective given that it was made by Cartin Company is also 6% or 0.06.

Therefore, the correct answer is C: 0.06

Answer 2

Let A be the event that the sensor is defective and let B be the event that the sensor is made by Cartin Company.

P(A / B) = 0.06