Hi Asirei!
I always recommend drawing a “Probability Tree” like the one on the left - it helps organize the decimals and clearly shows all possible paths. Each branch represents a machine (A, B, or C) and whether a product is good or defective. The decimals show the probabilities at each step. I also suggest highlighting the values we need to solve the problem and circling the final target probability: the chance that a defective product came from Machine C on your tree.
Here is the equation for the conditional probability we are solving for:
Pr(C | defect) = Pr(defect ∩ C) / Pr(defect)
This means: the probability a defective product came from Machine C equals the probability it came from C and is defective, divided by the total probability of a defect. "Given" (|) means we already know the product is defective, and "∩" means we're looking at the overlap (both from C and defective). Plug in the numbers, and you get 26.6%!
Let me know if you’d like to go over any part of it!
