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.

Explanation:

Step1: Identify probability of oil - change

The probability that a car needs an oil - change is $\frac{3}{5}$.

Step2: Identify conditional probability of tire - rotation given oil - change

The probability that a car needs a tire - rotation given that it needs an oil - change is $\frac{4}{7}$.

Step3: Use the formula for conditional probability

The probability that a car needs both an oil - change and a tire - rotation is the product of the probability of needing an oil - change and the conditional probability of needing a tire - rotation given an oil - change. So $P=\frac{3}{5}\times\frac{4}{7}$.

Step4: Calculate the product

$\frac{3}{5}\times\frac{4}{7}=\frac{3\times4}{5\times7}=\frac{12}{35}$.

Answer:

$\frac{12}{35}$