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Question
The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15. If the oil had to be changed, what is the probability that a new oil filter is needed?
Solution
Let A be the event of changing oil, B be the event of changing oil filter.
Given P(A) = 0.30
P(B) = 0.40
P(A ∩ B) = 0.15
Probability of new oil filter B needed when the oil A changed is
P(B/A) = `("P"("B" ∪ "A"))/("P"("A"))`
= `0.15/0.30`
= `15/30`
= `1/2`
= 0.5
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