Preheat oven to 325 degrees and line a muffin pan with cupcake liners. Set aside.
In a large bowl, mix together the eggs, oil and water. Add dry brownie mix and blend until a thick batter forms. Divide batter evenly between cupcake liners. Bake for 15 minutes, until the center is firm to the touch. Cool completely on a wire rack.
To make the frosting, blend the butter, yogurt and dry frosting mix in a large bowl until creamy. Divide frosting evenly into three small bowls then use red, blue and yellow dye to color frosting, mixing thoroughly to incorporate.
Place a piping bag or plastic ziplock bag into a glass, folding the ends of the bag over the edge. Use a spatula to place each color of frosting into the bag, twist the ends closed then use your hands and gently squeeze the bag of frosting to mix the colors.
Cut the tip of the piping bag with a scissors and pipe the colored frosting onto each brownie cupcake.