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%
Blank 1:
Blank 2:
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).
A. Based on the results of the survey, the probability that a student had blue eyes and wore glasses is 8%. So, a blue-eyed student wearing glasses is as rare as finding a unicorn with a rainbow-colored mane!
B. Looking at the data, we can see that out of the students who wear glasses, 24% have brown eyes. Therefore, the probability that a student's eye color is brown given that the student wears glasses is 24%. Seems like glasses have a thing for the color brown!
To calculate the probabilities, you need to find the relative frequency values in the two-way table.
A. The probability that a student had blue eyes and wore glasses is given by the relative frequency in the cell where "Eye Color" is blue and "Wears Glasses" is yes. Looking at the table, this value is 4%. Therefore, the answer is 4%.
B. The probability that a student's eye color is brown given that the student wears glasses is given by the relative frequency in the cell where "Eye Color" is brown and "Wears Glasses" is yes, divided by the total relative frequency for "Wears Glasses" is yes. Looking at the table, the probability of having brown eyes and wearing glasses is 16%. The total relative frequency for wearing glasses is yes (including all eye colors) is 24%. Therefore, the answer is (16% / 24%) = 0.67, rounded to the nearest tenth, which is 0.7 or 70%.
To find the probability in this two-way table, we need to use the relative frequencies provided.
A. To find the probability that a student had blue eyes and wore glasses, look at the intersection of the "Blue Eyes" row and "Glasses" column. The relative frequency in that cell is 8%. Therefore, the probability, rounded to the nearest tenth, is 8%.
Blank 1: 8%
B. To find the probability that a student's eye color is brown given that the student wears glasses, look at the "Wears Glasses" column. The sum of the relative frequencies in that column is 42.9%, indicating the proportion of students who wear glasses. Then, within that column, find the relative frequency for the "Brown Eyes" row, which is 16%. Therefore, the probability, rounded to the nearest tenth, is 16%.
Blank 2: 16%