probability and stastistics

the probability that an automobile filled with gasoline will also need an oil change is 25%.the probability that it needs a new filter is 40% and the probabilty that both the oil and filter need changing is 14%
a.)If the oil had to be change.What is the probabilty that a new oil filter is changed?
b.)If the new filter to be change.What is the probability that the new oil is changed?

Hello, alderon!

Use Bayes' Theorem: . $P(A \,|\,B) \;=\;\frac{P(A \cap B)}{P(B)}$

Quote:

The probability that a car will need an oil change is 25%.
The probability that it needs a new filter is 40%.
The probabilty that both the oil and filter need changing is 14%.

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

We are given: . $\begin{array}{ccc}P(\text{oil}) & = & 0.25 \\ P(\text{filter}) & = & 0.40 \\ P(\text{oil}\cap\text{filter}) & = & 0.14\end{array}$

$a)\;P(\text{filter}\cap\text{oil}) \;=\;\frac{P(\text{filter}\cap\text{oil})}{P(\text {oil})} \;=\;\frac{0.14}{0.25} \;=\;0.56$

$b)\;P(\text{oil}\cap\text{filter}) \;=\;\frac{P(\text{oil}\cap\text{filter})}{P(\text {filter})} \;=\;\frac{0.14}{0.40} \;=\;0.35$

thanks!!!

thanks...buddy...