Exercise 7 Page 694

We want to compare the percentage of the brown-haired students with blue eyes and the percentage of the red-haired students with brown eyes. To do so, we will first identify the number of $\text{brown-haired}$ $\text{students}$ $\text{with}$ $\text{blue}$ $\text{eyes,}$ the number of $\text{red-haired}$ $\text{students}$ $\text{with}$ $\text{brown}$ $\text{eyes,}$ and the $\text{grand}$ $\text{total}$ in the given two-way table. Let's do it!

		$\text{Hair Color}$
		Black	Brown	Red	Blond	Total
$\text{Eye Color}$
	Brown	$7$	$12$	$3$	$1$	$23$
	Blue	$2$	$8$	$2$	$9$	$21$
	Hazel	$2$	$5$	$1$	$1$	$9$
	Green	$1$	$3$	$1$	$2$	$7$
	Total	$12$	$28$	$7$	$13$	$60$

We can see in the table that there are $60$ students in total. Out of $60$ students, there are $8$ brown-haired students with blue eyes and $3$ red-haired students with brown eyes. We will now compare the percentages using the relative frequencies. To do so, we can calculate the ratio of each joint frequency to the grand total. We found that the frequency of brown-haired students with blue eyes is about $0.13,$ or $13\%.$ The frequency of red-haired students with brown eyes is $0.05,$ which can be also written as $5\%.$ Let's now compare the percentages!

• Out of all students, about $13\%$ of them have brown hair and blue eyes.
• Out of all students, $5\%$ of them have red hair and brown eyes.

We know that $13\%$ is greater than $5\%.$ This means that the percentage of red-haired students with brown eyes is greater than the percentage of brown-haired students with blue eyes.