Question

A car dealership has various combinations of vehicles in their car lot, all of which have an equally likely chance of being selected. Use the list of options below to determine the probability of each vehicle being selected.

What is the probability of selecting a silver vehicle with cloth interior?
What is the probability of selecting an SUV or a truck that is red or black with cloth interior?
What is the probability of selecting a sedan with cloth interior that is not red?
What is the probability of selecting a truck that is black or blue and has leather interior?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The probabilities of each of the following combination in question is 1/8, 1/6, 1/8, and 1/12 respectively.

The car dealership offers combinations of car parameters. The possible values of each car parameter are :

Vehicle = [Sedan, Suv, Truck]

Exterior color = [Red, Blue, Silver, Black]

Interior Material = [Leather, Cloth]

1. The probability of selecting a Silver Vehicle with a Cloth Interior is 1/8.

P(Silver, Cloth) = P(Exterior = Silver, Interior=Cloth)

                        = P(Exterior = Silver) * P(Interior=Cloth)

                        = (1/Total exterior options) * (1/Total interior options)

                        $= (1/4)*(1/2)$

                        $= 1/8$

2. The probability of selecting an SUV or Truck with a Red or Black color and Cloth Interior is 1/6.

P(SUV|Truck, Red|Black, Cloth)

                        = P(Vehicle=Suv|Truck, Exterior = Red|Black, Interior=Cloth)

                        =  P(Vehicle=Suv|Truck) * P(Exterior = Red|Black) * P(Interior=Cloth)

                        = (2/Total vehicle options) * (2/Total exterior options) * (1/Total interior options)

                        $= (2/3)*(2/4)*(1/2)$

                        $= 1/(3*2)$

                        $=1/6$

3. The probability of selecting a Sedan of a non-Red color and Cloth Interior is 1/8.

P(Sedan, !Red, Cloth)

                        = P(Vehicle=Sedan, Exterior != Red, Interior=Cloth)

                        =  P(Vehicle=Sedan) * (1- P(Exterior = Red)) * P(Interior=Cloth)

                        $= (1/3)*(1-(1/4))*(1/2)$

                        $= (1/3)*(3/4)*(1/2)$

                        $= 1/8$

4. The probability of selecting a Truck of a Blue or Black color and Leather Interior is 1/12.

P(Truck, Blue|Black, Leather)

                        = P(Vehicle=Truck, ExteriorBlue|Black, Interior=Leather)

                        =  P(Vehicle=Truck) * P(Exterior = Blue|Black)) * P(Interior=Leather)

                        $= (1/3)*(2/4)*(1/2)$

                        $= 1/12$

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