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

Explanation:

Step1: Calculate brown hair (brown eyes)

$0.80 \times 0.90 = 0.72$

Step2: Calculate brown hair (non-brown eyes)

$0.20 \times (1-0.20) = 0.20 \times 0.80 = 0.16$

Step3: Total brown hair frequency

$0.72 + 0.16 = 0.88$

Step4: Identify marginal frequencies

Marginal frequencies: brown eyes = 0.80, non-brown eyes = 0.20, brown hair = 0.88, non-brown hair = $1-0.88=0.12$

Answer:

0.88; Individuals with brown hair