Question

At Bob's Auto Plaza there are currently 11 new cars, 8 used cars, 12 new trucks, and 10 used trucks. Bob is going to choose one of these vehicles at random tobe the Deal of the Month. What is the probability that the vehicle that Bob chooses is used or is a car?Do not round intermediate computations, and round your answer to the nearest hundredth.

Answer 1

Let:

• A, be the event of Bob choosing an used vehicle

,

• B, be the event of Bob choosing a car

Now, we know that:

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

Out of the 41 vehicles, 18 are used. Therefore,

`P(A)=(18)/(41)`

Out of the 41 vehicles, 19 are cars. This way,

`P(B)=(19)/(41)`

Out of the 41 vehicles, 8 are used cars. Thereby,

`P(A\cap B)=(8)/(41)`

This way, we'll have that

`\begin{gathered} P(A\cup B)=(18)/(41)+(19)/(41)-(8)/(41) \\ \\ \Rightarrow P(A\cup B)=(29)/(41) \\ \\ \rightarrow P(A\cup B)=0.71 \end{gathered}`

Therefore, the probability that the vehicle that Bob chooses is used or is a car is aproximately 0.71