How to find probability using Bayes' theorem?

Question

A company has four production sections viz., S1 , S2 , S3 and S4 which contribute 30% , 20% , 28% and 22% of the total output. It was observed that those sections respectively produced 1% , 2% , 3% and 4% defective units. If a unit is selected at random and found to be defective, what is the probability that the unit so selected has come from either S1 or S4.

Answer 1

Hint: We know

$P(S_1)=0.30$, $P(S_2)=0.20$, $P(S_3)=0.28$, $P(S_4)=0.22$. If $D$ is the defect case than we know also $P(D|S_1)=0.01$, $P(D|S_2)=0.02$, $P(D|S_3)=0.03$,and $P(D|S_4)=0.04$.

Now, the question is asking you to determine $P(S_1|D) + P(S_4|D)$. Can you determine these probabilities with the Bayes' theorem?