What is the probability that a defective part came from supplier B?

[fireboy420]

The ABC manufacturing company purchases a certain part from two suppliers (A supplier & B supplier). The parts received from the suppliers are used to produce the company’s major product. The parts received from the suppliers are either defective or good parts. The A supplier provides 80% of all parts. Given that a part is from the A supplier, there is 2.5% probability that the part is defective. Given that a part is from the B supplier, there is a 1% chance that the part is defective.

a) If a defective part is found, what is the probability that it is from supplier B?
>>>(.025*.2)?
b) What is the probability that the company’s major product is defective?
>>>(.025*.2)+(.8*.01)?

 

[pmsrw3]

(b) looks right. You need to think a little harder about (a). Think about this: if a defective part is found, it must be from either A or B. So the probability that a defective part is from A and the probability that it is from B have to add up to 1. If you calculate the probability that a defective part is from A in the same way as you did for B, then add the two answers, do you get 1?

 

[fireboy420]

Thanks for your reply. Ur answer is still not clear to me. Sorry!

 

[pmsrw3]

What part don't you understand?

 

[fireboy420]

My understanding: (.8*.025)+(0.2*0.01)

But that doesn't add to 1.

 

[pmsrw3]

My understanding: (.8*.025)+(0.2*0.01)

But that doesn't add to 1.

Exactly. So that means you can't be calculating the conditional probability in the right way. Any calculation you try, you can do this check, and if it doesn't add up to 1, you know you need to think again.

Now, you know that the chance of a defect is (.025*.2)+(.8*.01). You know that in some of those cases the bad part was from company A, and in some it was from company B. What are the proportions?

 

[fireboy420]

Then isn't it what I had was right? (0.025*.2) since B is only 20% supplier.

 

[fireboy420]

sorry its 0.2*0.01 right?

 

[pmsrw3]

Then isn't it what I had was right? (0.025*.2) since B is only 20% supplier.

That's the proportion of bad B's in ALL the products, good and bad. What's the proportion of bad B's in just the bad products?

Try this: say we made 1000 products. How many of those contain the B part? How many contain a bad B part? How many contain an A part? How many contain a bad A part? What's the total number of bads in the 1000? Of those bads, how many are B's and how many are A's?