A store received a shipment of 1{,}000 MP3 players, 4 of which were defective. If an MP3 player is randomly...

1. TRANSLATE the problem information

• Given information:
  • Total MP3 players in the shipment: 1,000
  • Number of defective MP3 players: 4
  • We need to find the probability of randomly selecting a defective player
• What this tells us: This is a basic probability problem where we need favorable outcomes over total outcomes.

2. TRANSLATE the probability setup

• Favorable outcomes: 4 (the defective MP3 players)
• Total possible outcomes: 1,000 (all MP3 players in the shipment)
• Probability formula: \(\mathrm{P} = \frac{\mathrm{favorable\,outcomes}}{\mathrm{total\,outcomes}}\)

3. SIMPLIFY the calculation

• \(\mathrm{P(defective)} = \frac{4}{1000}\)
• Convert to decimal: \(4 \div 1000 = 0.004\)

Answer: A. 0.004

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students misread or misinterpret the total number of items, using 100 instead of 1,000 as the denominator.

They might think "4 out of 1,000" sounds like "4 out of 100" or mentally simplify too early, calculating \(\frac{4}{100} = 0.04\). This leads them to select Choice B (0.04).

Second Most Common Error:

Missing conceptual knowledge of probability: Students don't understand that probability requires a fraction or decimal between 0 and 1, instead thinking the answer is just the count of defective items.

They see "4 defective" and think that's the complete answer. This may lead them to select Choice D (4).

The Bottom Line:

This problem tests whether students can correctly identify the components of a probability calculation from a word problem. The key challenge is maintaining accuracy with the large numbers (1,000 vs 100) while applying the basic probability formula.