The probability of an automobile being filled with gasoline also needing an oil change is 0.25 ; the probability that it needs a new oil filter is $0.40 ;$ and the probability that both the oil and the filter need changing is 0.2 . (a) If the oil has to be changed, what is the probability that a new oil filter is needed? (b) If a new oil filter is needed, what is the probability that the oil has to be changed?
Added by Melissa P.
Step 1
So, P(Filter|Oil) = P(Oil and Filter) / P(Oil) = 0.2 / 0.25 = 0.8. Show more…
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