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

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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

Mathematics
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i honestly dont know
" 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"
Let's break this down
You need to name your events.
\(A\): it has a defect \(B\): it comes from Breaker \(C\): it comes from Cartin \(F\): it comes from Flutes
"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\[ \Pr(A|B) = 0.04 \]
"The Breaker's Manufacturing Company makes 80% of a particular sensor" This is saying "The probability a it comes from Breaker is 80%"\[ \Pr(B) = 0.80 \]
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.
i dont know how to use that
Did they teach you anything about probability? I'm using standard notation.
no they didnt
HI!!
hello (:
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?"
they tell you what it is, it is 6%
ok im gonna try it
it was right! thank you!

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