Question

Use the image to answer the question.

A Venn diagram with three intersecting circles is labeled with numbers. The top left circle is labeled “Geometry,” the top right circle is labeled “World History,” and the bottom circle is labeled “Pottery.”
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Inside the circle representing geometry is the number 321, inside the circle representing world history is the number 254, and inside the circle representing pottery is the number 61. Inside the area where geometry and pottery overlap is the number 100, inside the area where world history and pottery overlap is the number 52, and inside the area where geometry and world history overlap is the number 410. The area where all three circles overlap is the number 74.


A survey was conducted of the courses taken by the 1,272 sophomores at a local high school. Determine the probability that a student is currently taking geometry or pottery. State your answer as a fraction. You do not have to reduce the fraction.

(1 point)
Responses

1,0181,272

Start Fraction 1,018 over 1,272 End Fraction

2541,272

Start Fraction 254 over 1,272 End Fraction

9501,272

Start Fraction 950 over 1,272 End Fraction

100/1,272

Answer 1

We interpret the labeled numbers as the counts in each Venn region. Total taking geometry = 321+410+100+74 = 905. Total taking pottery = 61+100+52+74 = 287. Geometry∩Pottery = 100+74 = 174. So

|Geometry ∪ Pottery| = 905 + 287 − 174 = 1,018.

Probability = 1,018/1,272.