The table summarizes the distribution of major and year for 90 students in a program. Science Arts Total Freshman 20...

1. TRANSLATE the table information

• Given information:
  • Total science majors: 20 (freshmen) + 15 (sophomores) = 35 students
  • Total students in program: 90 students
  • Need: Probability of selecting a science major

2. INFER the probability approach

• This is asking for a basic probability: \(\mathrm{P(Science\ major)}\)
• Use the fundamental probability formula: \(\frac{\mathrm{favorable\ outcomes}}{\mathrm{total\ outcomes}}\)
• Favorable outcomes = science majors = 35
• Total outcomes = all students = 90

3. Set up and SIMPLIFY the probability fraction

• \(\mathrm{P(Science\ major)} = \frac{35}{90}\)
• Reduce to lowest terms by finding GCD of 35 and 90
• \(35 = 5 \times 7\), \(90 = 2 \times 3^2 \times 5\), so \(\mathrm{GCD} = 5\)
• \(\frac{35}{90} = \frac{7}{18}\)

4. Convert to decimal form

• \(\frac{7}{18} = 0.3888... \approx 0.389\)

Answer: \(\frac{7}{18}\) or 0.389

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread the table and use incorrect numbers. They might use 20 (freshman science majors only) instead of 35 (total science majors), or confuse rows and columns.

This leads them to calculate \(\mathrm{P} = \frac{20}{90} = \frac{2}{9} \approx 0.222\), giving an incorrect answer.

Second Most Common Error:

Inadequate SIMPLIFY execution: Students correctly identify the probability as \(\frac{35}{90}\) but fail to reduce it to lowest terms, leaving their answer as \(\frac{35}{90}\) or converting incorrectly to decimal form.

This causes them to provide \(\frac{35}{90}\) or an incorrect decimal like 0.35, missing the simplified form that many answer formats expect.

The Bottom Line:

Success requires careful table reading to identify the correct totals and consistent fraction simplification. The conceptual understanding is straightforward, but execution details determine accuracy.