Task 1

Consider the given joint probabilty distribution for a domain of two variables (Color, Vehicle) :

	Color = Red	Color = Green	Color = Blue
Vehicle = Car	0.1184	0.1280	0.0736
Vehicle = Van	0.0444	0.0480	0.0276
Vehicle = Truck	0.1554	0.1680	0.0966
Vehicle = SUV	0.0518	0.0560	0.0322

Part a: Calculate P ( Color is not Green | Vehicle is Truck )

Part b: Check if Vehicle and Color are totally independant from each other

Part A

Calculate P ( Color is not Green | Vehicle is Truck )

$=P(\frac{Color\ne Green}{Vehicle=Truck})$

$=\frac{P(Color\ne Green\wedge Vehicle=Truck)}{P(Vehicle=Truck)}$

$=\frac{0.1554+0.0966}{0.1554+0.1680+0.0966}=0.6$

Part B

Check if Vehicle and Color are totally independant from each other

$P(Color\ne Green)=1-P(Color=Green)$$P(Color\ne Green)=1-0.1280+0.0480+0.1680+0.0560$$P(Color\ne Green)=0.6$
$P(Color\ne Green)=P(\frac{Color\ne Green}{Vehicle=Truck})$

So Color & and Vehicle are independent from each other