Respuesta :
Answer:
The probability that a car that comes into the garage needs both an oil change and a tire rotation is [tex]\frac{12}{35}[/tex].
Step-by-step explanation:
The conditional probability of an event B given that another event A has already occurred is:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
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:
[tex]P(X)=\frac{3}{5}[/tex]
[tex]P(Y|X)=\frac{4}{7}[/tex]
Compute the value of P (X ∩ Y) as follows:
[tex]P(Y|X)=\frac{P(X\cap Y)}{P(X)}[/tex]
[tex]\frac{4}{7}=\frac{P(X\cap Y)}{3/5}[/tex]
[tex]P(X\cap Y)=\frac{4}{7}\times \frac{3}{5}[/tex]
[tex]=\frac{12}{35}[/tex]
Thus, the probability that a car that comes into the garage needs both an oil change and a tire rotation is [tex]\frac{12}{35}[/tex].
