Question

3. 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 0.40; and the probability that both the oil and the filter need changing is 0.14

(a) If a new oil filter is needed, what is the probability that the oil has to be changed
(b) If the oil has to be changed, what is the probability that a new oil filter is needed?

Answer 1

Let

probability of needing an oil be O

probability of needing an oil filter be F

$P(O)=0.25$

$P(F)=0.40$

$P(O\cap F)=0.14$

a. $P(O|F)$

$P(O|F)=\frac{P(O\cap F)}{P(F)}$

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

b. $P(F|O)$

$P(F|O)=\frac{P(O\cap F)}{P(O)}$

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