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.”

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

1001,272
Start Fraction 100 over 1,272 End Fraction

1,0181,272
Start Fraction 1,018 over 1,272 End Fraction

9501,272
Start Fraction 950 over 1,272 End Fraction

2541,272
Start Fraction 254 over 1,272 End Fraction
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1 answer

To determine the probability that a student is currently taking geometry or pottery, we need to find out how many students are taking either of those subjects (or both) based on the information from the Venn diagram.

  1. Let \( G \) be the total number of students taking Geometry.
  2. Let \( P \) be the total number of students taking Pottery.
  3. Let \( G \cap P \) be the number of students taking both Geometry and Pottery.

The probability \( P(G \cup P) \) that a student is taking either Geometry or Pottery is given by:

\[ P(G \cup P) = \frac{G + P - G \cap P}{\text{Total number of students}} \]

Without the actual numbers from the Venn diagram, let's assume we have counted the students taking Geometry and Pottery, along with those taking both, and we find the total number.

For the answer choices:

  • \( \frac{100}{1272} \)
  • \( \frac{1018}{1272} \)
  • \( \frac{950}{1272} \)
  • \( \frac{254}{1272} \)

You need to check the counts in the Venn diagram to plug these values into the formula above and determine which fraction correctly represents students taking Geometry or Pottery based on the survey data given.

Since we don’t have the exact numbers, I cannot determine which answer is correct without seeing the Venn diagram and having the specific counts. Please refer to the counts in the Venn diagram to find \( G, P, G \cap P \) to calculate the right answer.