7 a company manufacturing electronic components for home...

7. A company manufacturing electronic components for home entertainment systems buys electrical connectors from 3 suppliers. The company prefers to use supplier A because only 1% of those connectors prove to be defective, but supplier A can only deliver 65% of the connectors needed. The company must also purchase connectors from 2 other suppliers, 20% from supplier B and the rest from Supplier C. The rates of defective connectors from B and C are 2% and 4% respectively. Round off answers to 4 decimal places as necessary. A. Create a probability tree showing the probabilities of defectives and not defectives among the supplies delivered by 3 suppliers. B. You buy one of the components, and when you try to use it you find that the connector is defective. What is the probability that the component came from supplier A? C. Given that the component is not defective, what is the probability that it was delivered by supplier C?

Transcript

00:01 We're going to start this problem by creating a probability tree, showing the probabilities of defects and not defects among the supplies delivered by the three suppliers.

00:13 So a company manufacturing electronic components for home entertainment systems buys electrical contractors from c3 suppliers, supplier a, supplier b, and supplier c.

00:30 Supplier a can only deliver 65 % of the components needed.

00:38 Whereas the company must also purchase connectors from the two other suppliers, 20 % comes from supplier b and the rest come from supplier c.

00:50 So the 65 and the 20 add up to 85%.

00:54 So that means there's 15 % that has to come from supplier c.

00:58 Now, this company liked supplier a because when a delivers, they only deliver with a defective rate of 0 .01 or 1%.

01:13 So that means not defective is 99 % of the time.

01:21 Whereas supplier 2 or supplier b has a 2 % defective rate, which means that not defective is going to be 98 % and supplier c has a defective rate of 4%.

01:41 So that means they're not defective rate is 96%.

01:47 So that's your answer for part a where we had to construct the probability tree.

01:54 For part b we want to use this tree and we want to find a probability.

01:58 So for part b, you buy one of the components and when you try to use it, you find that the connector is defective.

02:10 And we want to know what's the probability that the component came from supplier a.

02:15 So we're looking for the probability of coming from supplier a, given that we know that it is defective.

02:23 So in this case, we are going to have to think about the formula for dependent probability.

02:33 And for dependent probability, the probability of event a, and then event b is equal to the probability of event a happening, multiplied by the probability of b happening given that we know that a has already occurred.

02:52 So our problem looks like this part of the formula.

02:57 So if i can isolate that part, i can then utilize the new formula to help us solve this problem.

03:05 So i'm going to divide by the probability of a on both sides.

03:12 So the probability of event b happening, given that a has already occurred, is equal to the probability of event a and event b happening divided by the probability of event a.

03:26 So in our scenario, our event a is our defective, and our event b is that.

03:38 That it's coming from supplier a.

03:42 So therefore, we could expand this out and say the probability of coming from supplier a and being defective divided by the probability of being defective.

03:54 So the probability of coming from a and defective will be these two multiplied together...

Question

Please give Ace some feedback