At a community event, each of the 375 attendees registers for exactly one of three workshops: Java, Python, or Data....

1. TRANSLATE the problem information

• Given information:
  • Total attendees: 375
  • \(\mathrm{P(not\ Python)} = 0.76\)
  • \(\mathrm{P(Java)} = \frac{7}{20} = 0.35\)
  • Each person registers for exactly one workshop

• What we need to find: Number of attendees who registered for Python

2. INFER the key relationship

• Since we know \(\mathrm{P(not\ Python)} = 0.76\), we can find \(\mathrm{P(Python)}\) using the complement rule
• The complement rule tells us: \(\mathrm{P(Python)} + \mathrm{P(not\ Python)} = 1\)
• Therefore:
  \(\mathrm{P(Python)} = 1 - \mathrm{P(not\ Python)}\)
  \(\mathrm{P(Python)} = 1 - 0.76\)
  \(\mathrm{P(Python)} = 0.24\)

3. SIMPLIFY to find the final count

• Number who registered for Python = \(\mathrm{P(Python)} \times \mathrm{Total\ attendees}\)
• Number = \(0.24 \times 375 = 90\) (use calculator)

4. INFER a verification check

• We can verify our answer makes sense:
• \(\mathrm{P(Data)} = 1 - \mathrm{P(Java)} - \mathrm{P(Python)}\)
  \(\mathrm{P(Data)} = 1 - 0.35 - 0.24\)
  \(\mathrm{P(Data)} = 0.41\)
• Check: \(0.35 + 0.24 + 0.41 = 1.00\) ✓

Answer: C. 90

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students might misinterpret "probability that a randomly selected attendee did not register for Python is 0.76" and think this directly gives them \(\mathrm{P(Python)} = 0.76\), rather than recognizing this is \(\mathrm{P(not\ Python)}\).

If they use 0.76 as \(\mathrm{P(Python)}\), they would calculate \(0.76 \times 375 = 285\) attendees, which isn't even among the answer choices, leading to confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students understand the complement rule correctly and find \(\mathrm{P(Python)} = 0.24\), but make calculation errors when computing \(0.24 \times 375\).

Common mistakes include getting 72 or 84 through computational errors. This may lead them to select Choice A (72) or Choice B (84).

The Bottom Line:

This problem tests whether students can correctly interpret probability language (especially complement events) and accurately convert probabilities to counts. The key insight is recognizing that "did not register for Python" gives you the complement probability, not the direct probability.