*Edited* (thanks Alex!)
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?
of the girls,
brown: 4/5
long brown: 3/4 * 4/5 = 3/5
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To find the fraction of girls in the class who have long brown hair, we need to multiply the fractions that represent each condition.
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.