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 Breaker’s

Answer 1

Let's set the unknown value as x.
\[x=\frac{ 0.8 \times 0.04 }{ 0.8 \times 0.04 + 0.15 \times 0.06 + 0.05 \times 0.09 }\]

Answer 2

The amount that is defective made by Breaker's Company is on the top, and the bottom is the total amount of sensors that are defective. Once you solve the equation, the fraction is the probability of a defected sensor being a Breaker Company defected sensor :)