Question

At Sanger’s auto garage, three out of every five cars brought in for service need an oil change. Of the cars that need an oil change, four out of every seven also need a tire rotation.

What is the probability that a car that comes into the garage needs both an oil change and a tire rotation? Give the answer in fraction form.

Answer 1

12/35

Explanation:

Answer 2

The probability that a car that comes into the garage needs both an oil change and a tire rotation is
`(12)/(35)`.

Explanation:

The conditional probability of an event B given that another event A has already occurred is:

`P(B|A)=(P(A\cap B))/(P(A))`

Denote the events as follows:

X = cars brought in for service need an oil change

Y = cars brought in for service need a tire rotation

The information provided is:

`P(X)=(3)/(5)`

`P(Y|X)=(4)/(7)`

Compute the value of P (X ∩ Y) as follows:

`P(Y|X)=(P(X\cap Y))/(P(X))`

`(4)/(7)=(P(X\cap Y))/(3/5)`

`P(X\cap Y)=(4)/(7)* (3)/(5)`

`=(12)/(35)`

Thus, the probability that a car that comes into the garage needs both an oil change and a tire rotation is
`(12)/(35)`.