A workshop has three machines. Machine P makes 25% of the parts, machine Q makes 35% and machine R…

Step 1. The paths. $P$: $0.25 \times 0.04 = 0.01$. $Q$: $0.35 \times 0.02 = 0.007$. $R$: $0.40 \times 0.01 = 0.004$.

Step 2. The total. $0.01 + 0.007 + 0.004 = 0.021$.

Step 3. The posteriors. $\dfrac{0.01}{0.021} = \dfrac{10}{21} \approx 0.4762$. $\dfrac{0.007}{0.021} = \dfrac{1}{3} \approx 0.3333$. $\dfrac{0.004}{0.021} = \dfrac{4}{21} \approx 0.1905$.