JEE Advanced 2025 — Paper 2 — Question 27

A factory has a total of three manufacturing units, $M_{1}, M_{2}$, and $M_{3}$, which produce bulbs independent of each other. The units $M_{1}, M_{2}$, and $M_{3}$ 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 $M_{1}, 15 \%$ 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 $M_{2}$ is $\frac{2}{5}$. If a bulb is chosen randomly from the bulbs produced by $M_{3}$, then the probability that it is defective is $\qquad$