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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 a new oil filter is needed, what is the probability that the oil has to be changed?
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Solution
Let A be the event of changing oil, B be the event of changing oil filter.
Given P(A) = 0.30
P(B) = 0.4
P(A ∩ B) = 0.15
Probability of oil A changed when new oil filter B is changed is P(A/B) = `("P"("A" ∩ "B"))/("P"("B"))`
= `0.15/0.40`
= `15/40`
= `3/8`
= 0.375
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