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

• fireboy420
In summary, the ABC manufacturing company purchases a certain part from two suppliers. 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 a 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.
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)?

(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?

What part don't you understand?

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

But that doesn't add to 1.

fireboy420 said:
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?

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

sorry its 0.2*0.01 right?

fireboy420 said:
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?

## 1. What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint occurrence of both events by the probability of the first event occurring alone.

## 2. How is conditional probability different from regular probability?

Regular probability deals with the likelihood of an event occurring without any additional information. Conditional probability takes into account other factors, such as the occurrence of another event, when determining the likelihood of an event.

## 3. Can you provide an example of conditional probability?

One example of conditional probability is the likelihood of a student passing a test given that they studied for at least 3 hours. This takes into account the additional information of the student's study time when determining the probability of passing the test.

## 4. How is conditional probability used in real life?

Conditional probability is used in many real-life scenarios, such as weather forecasting, medical diagnosis, and risk assessment in insurance. It helps to make more accurate predictions and decisions by taking into account other relevant factors.

## 5. What is the formula for calculating conditional probability?

The formula for conditional probability is P(A|B) = P(A and B) / P(B), where P(A|B) is the conditional probability of event A given event B, P(A and B) is the joint probability of both events occurring, and P(B) is the probability of event B occurring alone.

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