of the girls,
brown: 4/5
long brown: 3/4 * 4/5 = 3/5
In a class, 4/5 of the girls have brown hair. Of the brown-haired girls, 3/4 of the have long hair. Of the girls with long brown hair, 1/3 of them have green eyes.
Question: What fraction of the girls in the class have long brown hair?
brown: 4/5
long brown: 3/4 * 4/5 = 3/5
First, let's determine the fraction of girls in the class who have brown hair. We're given that 4/5 of the girls have brown hair.
Next, we need to find the fraction of brown-haired girls who have long hair. We know that 3/4 of the brown-haired girls have long hair. Therefore, we multiply 4/5 (brown-haired girls) by 3/4 (girls with long hair).
Finally, we need to determine the fraction of the girls with long brown hair who have green eyes. We're given that 1/3 of the girls with long brown hair have green eyes. So, we multiply the fraction we got in the previous step (4/5 * 3/4) by 1/3.
Let's calculate it step by step:
Fraction of girls with brown hair = 4/5
Fraction of brown-haired girls with long hair = (4/5) * (3/4) = 12/20 = 3/5
Fraction of girls with long brown hair and green eyes = (3/5) * (1/3) = 3/15 = 1/5
Therefore, 1/5 of the girls in the class have long brown hair.