A high school class conducts a survey where students are asked about their eye color and whether or not they wear glasses. The two-way table below shows the results of the survey as relative frequencies.

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A. Based on thee results of the survey, what is the probability, rounded to the nearest tenth, that a student had blue eyes and wore glasses?

B. Based on the results of the survey, what is the probability, rounded to the nearest tenth, that a student's eye color is brown given that the student wears glasses?

Word Bank:
12% 8% 4% 42.9% 24% 16% 20%
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1 answer

A. The relative frequency for blue eyes and glasses is 0.08, which is 8%. Therefore, the probability that a student had blue eyes and wore glasses is 8%, or 0.08 (rounded to the nearest tenth).

B. The relative frequency for students who wear glasses and have brown eyes is 0.16, which is 16%. The relative frequency for all students who wear glasses is 0.4, which is 40%. Therefore, the conditional probability that a student's eye color is brown given that the student wears glasses is:

P(brown eyes | wears glasses) = P(brown eyes and wears glasses) / P(wears glasses)

P(brown eyes | wears glasses) = 0.16 / 0.4

P(brown eyes | wears glasses) = 0.4

So, the probability that a student's eye color is brown given that the student wears glasses is 40%, or 0.4 (rounded to the nearest tenth).