Couple of trees, if it helps. (It definitely should!) Converting probabilities to frequencies also helps in switching the priorities, as shown.
See also Bayes' theorem - Wikipedia, the free encyclopedia
A electrician regularly purchases a particular type of electrical component.that it was supplied by company A?
60% are purchased from company A, and 40 % are from Company B.2% of those supplied by company A and 1% of those supplied byCompany B are known to be defective.
The components are identical and thoroughly mixed on receipt. If a component is selected at randomi) What is the probability that this component was supplied bycompany A and was defective?(ii) Calculate the probability that the component was defective.(iii) Given that the component was defective, what is the probability
Also notice each tree is kind of like a venn diagram, which can also help.
"(iii) Given that the component was defective, what is the probability
that it was supplied by company A?"
Here is how I would do this: suppose there were 1000 components. 60% of them are from A so 600 are from A. 40% are from B so 400 are from B. 2% of those from A, 2% of 600= 12 are defective. 1% of those from B, 1% of 400= 4 are defective. That makes a total of 16 defective components, 12 of which are from A. Given that a component is defective, the probability it is from A is 12/16= 3/4= 0.75.