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The probability that a car has a certain factory defect is 825. The probability that a car has a certain factory defect and needs an oil change is 750. What is the probability that a car needs an oil change given that it has a certain factory defect

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Answer:

90.91% probability that a car needs an oil change given that it has a certain factory defect

Explanation:

We use the conditional probability formula to solve this question. It is


P(B|A) = (P(A \cap B))/(P(A))

In which

P(B|A) is the probability of event B happening, given that A happened.


P(A \cap B) 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
P(A) = 0.825

The probability that a car has a certain factory defect and needs an oil change is 750.

So
P(A \cap B) = 0.75

What is the probability that a car needs an oil change given that it has a certain factory defect


P(B|A) = (P(A \cap B))/(P(A)) = (0.75)/(0.825) = 0.9091

90.91% probability that a car needs an oil change given that it has a certain factory defect

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