Question

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

Answer 1

@misssunshinexxoxo

Answer 2

@beginnersmind

Answer 3

Which do you believe it is?

Answer 4

i honestly dont know

Answer 5

"
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"

Answer 6

Let's break this down

Answer 7

You need to name your events.

Answer 8

\(A\): it has a defect
\(B\): it comes from Breaker
\(C\): it comes from Cartin
\(F\): it comes from Flutes

Answer 9

"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\[
\Pr(A|B) = 0.04
\]

Answer 10

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

Answer 11

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.

Answer 12

i dont know how to use that

Answer 13

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

Answer 14

no they didnt

Answer 15

@beginnersmind

Answer 16

HI!!

Answer 17

hello (:

Answer 18

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?"

Answer 19

they tell you what it is, it is 6%

Answer 20

ok im gonna try it

Answer 21

it was right! thank you!