Respuesta :
Answer:
90.91% probability that a car needs an oil change given that it has a certain factory defect
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this problem, we have that:
Event A: having a factory defect.
Event B: needing an oil change.
The probability that a car has a certain factory defect is 825.
So [tex]P(A) = 0.825[/tex]
The probability that a car has a certain factory defect and needs an oil change is 750.
So [tex]P(A \cap B) = 0.75[/tex]
What is the probability that a car needs an oil change given that it has a certain factory defect
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.75}{0.825} = 0.9091[/tex]
90.91% probability that a car needs an oil change given that it has a certain factory defect
