31 1cas 77. ogy light trucks sad 45 3. Motor vehicles sold to individuals are classified as either cars or light trucks (including SUVs) and as either domestic or imported. In a recent year, 69% of vehicles sold were light trucks, 78% were domestic, and 55% were domestic light trucks. Let A be the event that a vehicle is a car, and B the event that it is imported. Write each of the following events in set notation and give its probability. a. The vehicle is a light truck. T:truck (1 pt) P (A' ) = PCT ) = 1 - PCA ) = 1-0.31 = 0169 b. The vehicle is an imported car. P ( B ) = P(AND ) + P ( AnB ) Can (2 pts) = ( 0 . 31 ) ( 0.7 7 ) + ( 0 . 69) ( 0 .45 ) = ora38+10 3165 0 15492 2 c. Given that a vehicle is imported, what is the probability it is a light truck? (2 pts) P ( A' / B ) = PCA'nB) = (0. 69 ( 0. 45) PCB ) Q: 5492 6 .565 - 1.5 d. Are the events "Vehicle is a light truck" and "vehicle is imported" independent? Mutually exclusive? (2 pts) Justify your answer. P (AIB ) = PCA) ( ) . - 1.5 xclusive