00:01
Alright, you have two questions here that use the same starting information, just different questions at the end.
00:07
So i want to organize this information, and i feel the best way to organize this information is to use a tree diagram.
00:14
We have our three companies, factories, that are producing this product.
00:19
We have factory a, factory b, and factory c.
00:24
Now, it doesn't directly tell you what the proportion is that each company makes, but it does tell you that a makes four times the amount of b, and b and c are the same.
00:38
So let's just say for a minute, i'll do that off to the side, that b and c both produce, they produce the same, let's say they produce x amount of this product.
00:52
A would be four times that, or 4x.
00:56
Now we could actually get the probability, since the total product here would be 6x, we know that a makes 4x of it, we get the probability of a being two thirds.
01:12
And then the other two would be x over 6x, which would be one sixth.
01:18
So we have the proportion for each factory, or you could call that a probability that a product comes from that factory.
01:27
Now, once it does go on to say that there's a certain defective rate, so we have a's defective rate, i'm going to say d, and nd will be not defective.
01:44
Looking at company a, it says 10 % are going to be defective, that would be 0 .1.
01:50
Not defective then would be 90 % from that company, or 0 .9.
01:55
For b's defective rate, we have 7%, so 0 .07, not defective, then would be 93 % or 0 .93.
02:08
For company c, or factory c, the defective would be 3%, not defective, 0 .97 or 97%.
02:23
Now looking at your question, it says, what is the probability that the selected item is defective? so basically we're going to pick one item at random after all of them have been stocked.
02:35
To figure out the defective rate, we need to multiply out any row, any set of branches that lead to defective, and then we'll add all those probabilities together for question number three.
02:50
So starting off, i'll take two thirds, and they want this answer correct to two decimal places.
02:57
So two thirds, and then i'm multiplying that by 0 .1, and that's going to give me 0 .0667...