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A study shows that 80% of the population of a city have brown eyes and 20% do not. The study also shows that 30% 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?

0.72; Individuals with brown eyes
0.80; Individuals with brown eyes
0.86; Individuals with brown hair
0.90; Individuals with brown hair

1 Answer

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Answer: The largest marginal relative frequency is 0.90 and it represents the probability of an individual having brown hair given that they have brown eyes.

Explanation:

The reason why 0.90 represents the probability of an individual having brown hair given that they have brown eyes is because the study shows that 90% of the people who have brown eyes also have brown hair. This is a conditional probability, which means that it is the probability of one event happening given that another event has already happened. In this case, the event of having brown hair is conditional on the event of having brown eyes. The probability of 0.90 is calculated by taking the total number of individuals with brown eyes and brown hair and dividing it by the total number of individuals with brown eyes. The number is large because 90% of the individuals with brown eyes have brown hair, it is the largest because it is the highest probability among the other marginal relative frequencies. This indicates that the majority of people with brown eyes also have brown hair

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