Question

The probability that an automobile being filled with gasoline also needs an oil change is 0.25; the probability that it needs a new oil filter is 0.35, and the probability that both the oil and the filter need changing is 0.14. If the oil has to be changed, what is the probability that a new oil filter is needed?

Answer 1

To find the probability that a new oil filter is needed, given that the oil needs to be changed, we can use conditional probability by dividing the probability that both the oil and filter need changing by the probability that the oil needs changing.

Step-by-step explanation:

To find the probability that a new oil filter is needed, we can use conditional probability. Given that the oil needs to be changed, we are looking for the probability that the filter also needs to be changed. Using the formula for conditional probability: P(A|B) = P(A and B) / P(B)

To find the probability that a new oil filter is needed, given that the oil needs to be changed, we can use conditional probability by dividing the probability that both the oil and filter need changing by the probability that the oil needs changing. The result is a probability of 0.56, meaning there is a 56% chance that a new oil filter is needed when the oil needs to be changed.

We are given that the probability that both the oil and filter need changing is 0.14, and the probability that the oil needs changing is 0.25. Therefore, P(oil and filter) = 0.14 and P(oil) = 0.25. Plugging these values into the formula, we get: P(filter|oil) = P(oil and filter) / P(oil) = 0.14 / 0.25 = 0.56.

Therefore, the probability that a new oil filter is needed, given that the oil needs to be changed, is 0.56.