Question

A study shows that 80% of the population of a city have brown eyes and 20% do not. The study also shows that 20% of the people who do not have brown eyes do not have brown hair, while 90% of the people who have brown eyes have brown hair. A relative frequency table was constructed for this data. What is the largest marginal relative frequency and its interpretation?

0. 90; Individuals with brown hair

0. 88; Individuals with brown hair

0. 80; Individuals with brown eyes

0. 72; Individuals with brown eyes

Answer 1

(b) 88%, individuals with brown hair

Explanation:

You want the largest marginal relative frequency in the two-way table showing relative frequencies of brown hair and brown eyes. You are given that 80% of the population has brown eyes, and 90% of those have brown hair. 20% of the 20% of people who do not have brown eyes do not have brown hair.

Table

The attachment shows the filled table. The marginal relative frequencies are the totals at the right and bottom edges. The largest of these is 88%, representing the proportion of the population with brown hair.

The largest marginal relative frequency is 88%, the fraction of individuals with brown hair, choice B.

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