anonymous one year ago The Breaker's Manufacturing Company makes 80% of a particular sensor, the Cartin Company makes 15% of them, and the Flutes Company makes the other 5%. The sensors made by Breaker's have a 4% defect rate, the Cartin sensors have a 6% defect rate, and the Flutes sensors have a 9% defect rate. If a sensor is randomly selected from the general population of all sensors, what is the probability that it is defective, given that it was made by Cartin Company? 0.04 0.05 0.06 0.15

1. anonymous

@misssunshinexxoxo

2. anonymous

@beginnersmind

3. misssunshinexxoxo

Which do you believe it is?

4. anonymous

i honestly dont know

5. misssunshinexxoxo

" 80% of a particular sensor, the Cartin Company makes 15% of them, and the Flutes Company makes the other 5%. The sensors made by Breaker's have a 4% defect rate, the Cartin sensors have a 6% defect rate, and the Flutes sensors have a 9% defect rate"

6. misssunshinexxoxo

Let's break this down

7. anonymous

You need to name your events.

8. anonymous

$$A$$: it has a defect $$B$$: it comes from Breaker $$C$$: it comes from Cartin $$F$$: it comes from Flutes

9. anonymous

"The sensors made by Breaker's have a 4% defect rate" This is saying "It it comes from Breaker, then the probability it has a defect is 4%", which means$\Pr(A|B) = 0.04$

10. anonymous

"The Breaker's Manufacturing Company makes 80% of a particular sensor" This is saying "The probability a it comes from Breaker is 80%"$\Pr(B) = 0.80$

11. anonymous

We want to use the conditional probability here, which states:$\Pr(A|B) = \frac{\Pr(A\cap B)}{\Pr(B)} \implies \Pr(A\cap B) = \Pr(A|B)\times \Pr(B)$Then we can use total probability:$\Pr(A) = \Pr(A\cap B) + \Pr(A\cap C) + \Pr(A \cap F)$This words because $$B\cup C\cup F$$ will make up the entire sample space.

12. anonymous

i dont know how to use that

13. anonymous

Did they teach you anything about probability? I'm using standard notation.

14. anonymous

no they didnt

15. anonymous

@beginnersmind

16. misty1212

HI!!

17. anonymous

hello (:

18. misty1212

this question is not that hard in fact, it is like "who is buried in grant's tomb" " the Cartin sensors have a 6% defect rate," "what is the probability that it is defective, given that it was made by Cartin Company?"

19. misty1212

they tell you what it is, it is 6%

20. anonymous

ok im gonna try it

21. anonymous

it was right! thank you!