JEE Advanced 2025 Mathematics question

A factory has a total of three manufacturing units, , , and , which produce bulbs independent of each other. The units , , and produce bulbs in the proportions of 2 : 2 : 1, respectively. It is known that 20% of the bulbs produced in the factory are defective. It is also known that, of all the bulbs produced by , 15% are defective. Suppose that, if a randomly chosen bulb produced in the factory is found to be defective, the probability that it was produced by is . If a bulb is chosen randomly from the bulbs produced by , then the probability that it is defective is .