In a factory, two machines $M1$ and $M2$ manufacture $60\%$ and $40\%$ of the autocomponents respectively. Out of the total production, $2\%$ of $M1$ and $3\%$ of $M2$ are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by $M2$?

How both questions solving method is same?? one is giving percentage from total production...

In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a randomly drawn autocomponent from the combined lot is found defective, what is the probability that it was manufactured by M2?

An automobile plant contracted to buy shock absorbers from two suppliers X and Y . X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable.Of X′s shock absorbers, 96% are reliable. Of Y′s shock absorbers, 72% are reliable.

Let $P(M_i)$ denote the probability that the component is manufactured by machine $M_i$, and $P(def)$ denote the probability that the component is defective.

Let there be 100 auto components. 60 of them are manufactured by M1 and 40 by M2. Total defective components will be 2.4 in total, 1.2 from each of M1 and M2 respectively. Then . .

The Red Crossed Out Arrow are none of our concern. Our concern is on defective components (2.4). Out of all defective components, probability that it was manufactured by M2 is = (1.2/2.4) = 0.5