Question

At a certain car dealership, 20% of customers who bought a new vehicle bought an SUV, and 3% of them bought a black SUV (that is 3% of customers bought a vehicle that was an SUV and in black color). Given that a customer bought an SUV, what is the probability that it was black?

Answer 1

Answer:  0.15

Step-by-step explanation:

As per given , the probability that customers who bought a new vehicle bought an SUV : P(SUV) = 0.20

The probability that customer bought a vehicle that was an SUV and in black color : P(SUV and black)  =0.03

Now by suing conditional probability formula,

If we have given that a customer bought an SUV, then the probability that it was black will be :

$\text{P(Black}|\text{SUV})=\dfrac{\text{P(SUV and Black)}}{\text{P(SUV)}}$

$=\dfrac{0.03}{0.20}=\dfrac{3}{20}=0.15$

Hence, the required probability is 0.15.