In a group, 40% of the items are red. Of all the red items in the group, 30% also have...

1. TRANSLATE the problem information

• Given information:
  • 40% of all items are red
  • 30% of the red items also have stripes

• What we need to find: What percentage of ALL items are red with stripes?

2. INFER the approach

• Key insight: We're looking for items that satisfy BOTH conditions (red AND striped)
• Since 30% refers to "of the red items," we need to find what 30% of the red items represents as a percentage of the total group
• Strategy: Multiply the two percentages together

3. SIMPLIFY the calculation

• Convert to decimals for easier multiplication:
  • Red items: \(40\% = 0.40\)
  • Striped red items: 30% of red = \(0.30\)

• Items that are red with stripes = \(0.30 \times 0.40 = 0.12\)

• Convert back to percentage: \(0.12 = 12\%\)

Answer: B. 12%

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misunderstand what "30% of red items" means in relation to the total group. They think they should add or subtract the percentages rather than multiply them.

Common incorrect reasoning: "40% are red and 30% have stripes, so either \(40\% + 30\% = 70\%\) or \(40\% - 30\% = 10\%\) are red with stripes."

This may lead them to select Choice A (10%) or Choice C (70%)

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly identify that multiplication is needed but get confused about what to multiply. They might calculate what percentage 30% is of 40% (\(30 \div 40 = 75\%\)) instead of 30% times 40%.

This reasoning leads them to select Choice D (75%)

The Bottom Line:

This problem tests whether students understand that when one condition depends on another (stripes depend on being red first), they must use multiplication, not addition or subtraction, to find the compound probability.