2022-05-08

The probability that an automobile being filled with gasoline will also need 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 filter need changing is 0.14. (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?

karton

Expert2022-08-01Added 613 answers

Let

probability of needing an oil be O

probability of needing an oil filter be F

$P\left(O\right)=0.25$

$P\left(F\right)=0.40$

$P(O\cap F)=0.14$

**a. **$P(F\mid O)$

$P(F\mid O)=\frac{P(O\cap F)}{P\left(O\right)}$

$=\frac{0.14}{0.25}=0.56$

**b. **$P(O\mid F)$

$P(O\mid F)=\frac{P(O\cap F)}{P\left(F\right)}$

$=\frac{0.14}{0.4}=0.35$

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