Question

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

Answer 1

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

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

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

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.75}{0.825} = 0.9091$

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