1. ## Probability

A electrician regularly purchases a particular type of electrical component.
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
that it was supplied by company A?

2. ## Re: Probability

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

3. ## Re: Probability

maybe im just tired but still not following sorry

4. ## Re: Probability

Originally Posted by gordonmckee
A electrician regularly purchases a particular type of electrical component. 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
that it was supplied by company A?
i) $P(A\cap D)=P(D|A)P(A)=~?$.

ii) $P(D)=P(D\cap A)+P(D\cap B)=~?$

iii) $P(A|D)=~?$

5. ## Re: Probability

Originally Posted by gordonmckee
[LEFT](i) What is the probability that this component was supplied bycompany A and was defective?
So walk through the (first) tree from the root, along the company A branch, which takes up 60% of the components, e.g. 60% of a million, and then on along the branch of defectives, which is 2% of the 600,000. What's the resulting 12,000 as a proportion of the whole million?

Originally Posted by gordonmckee
[LEFT](ii) Calculate the probability that the component was defective.
That'll be the 12,000 just mentioned plus the 4,000 other defectives which come from company B. Total them up. What's that as a proportion of the whole million?

Originally Posted by gordonmckee
(iii) Given that the component was defective, what is the probability
that it was supplied by company A?
Of the 16,000 defectives, how many are from company A? And what proportion of the 16,000 is that?

Also notice each tree is kind of like a venn diagram, which can also help.

6. ## Re: Probability

"(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.