I want to find the number of cars that are 4-door and red, so I will use a Venn diagram to represent the different categories of cars. I will draw two circles, one for the color (red or white) and one for the number of doors (2 or 4). The circles will overlap in four regions: red and 2-door, red and 4-door, white and 2-door, and white and 4-door. I will label each region with the number of cars in it, and I will use the given information to find the missing numbers. I know that $\frac{1}{3}$ of the cars are red, so that means 10 cars are red and 20 cars are white. I also know that $50\%$ of the cars are 4-door, so that means 15 cars are 4-door and 15 cars are 2-door. I also know that 8 cars are 2-door and white, so I will put 8 in the region where the white circle and the 2-door circle overlap. Now I have three regions filled in, and I can use them to find the other numbers. Since 8 cars are 2-door and white, and 15 cars are 2-door in total, that means 7 cars are 2-door and red. I will put 7 in the region where the red circle and the 2-door circle overlap. Since 7 cars are 2-door and red, and 10 cars are red in total, that means 3 cars are 4-door and red. I will put 3 in the region where the red circle and the 4-door circle overlap. Since 3 cars are 4-door and red, and 15 cars are 4-door in total, that means 12 cars are 4-door and white. I will put 12 in the region where the white circle and the 4-door circle overlap. Now I have all four regions filled in, and I can check that they add up to 30 cars in total. 8 + 7 + 3 + 12 = 30, so I have not made any mistakes. The question asks for the number of cars that are 4-door and red, and I have found that to be 3.


There are 30 cars in my building's parking lot.  All of the cars are red or white, and a car can have either 2 doors or 4 doors. $\frac{1}{3}$ of them are red, $50\%$ of them are 4-door, and 8 of them are 2-door and white.  How many of the cars are 4-door and red?