6. enVision STEM Hair color is an inherited trait. In Marci's family, her mother has brown hair. Her father has blond hair. The family has 6 children in all. Of the 6 children, \( \frac{1}{3} \) of them have blond hair, \( \frac{1}{6} \) of them have red hair, and \( \frac{1}{2} \) of them have brown hair. What fraction of the children have red or brown hair?

In Marci's family, there are a total of 6 children. To find out how many have red or brown hair, we first determine the number of children with each hair color. One-third of the children have blond hair, which means \( \frac{1}{3} \times 6 = 2 \) children have blond hair. One-sixth of the children have red hair, so \( \frac{1}{6} \times 6 = 1 \) child has red hair. Half of the children have brown hair, therefore \( \frac{1}{2} \times 6 = 3 \) children have brown hair. Now, to find the fraction of children with red or brown hair, we add the number of children with red hair (1) and brown hair (3): 1 (red) + 3 (brown) = 4 children. Thus, the fraction of children with red or brown hair is: \[ \frac{4}{6} = \frac{2}{3} \] So, \( \frac{2}{3} \) of the children have either red or brown hair.