A band with 45 members has 11 members who play saxophone. If one band member is selected at random, what...

1. TRANSLATE the problem information

• Given information:
  • Total band members: 45
  • Members who play saxophone: 11
  • We want: probability of randomly selecting a saxophone player

2. INFER the approach

• This is asking for probability, so we need the probability formula
• Probability = (favorable outcomes) ÷ (total outcomes)
• Here, favorable outcomes = selecting a saxophone player
• Total outcomes = selecting any band member

3. Apply the probability formula

• Favorable outcomes = 11 (saxophone players)
• Total outcomes = 45 (all band members)
• Probability = \(\frac{11}{45}\)

Answer: B. \(\frac{11}{45}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skills: Students misidentify what represents "favorable outcomes"

Instead of focusing on saxophone players (what we want), they might focus on non-saxophone players. They calculate \(45 - 11 = 34\), then write \(\frac{34}{45}\).

This may lead them to select Choice C (\(\frac{34}{45}\))

Second Most Common Error:

Conceptual confusion about probability: Students think probability should relate to "one person being selected" rather than the characteristic we're looking for

They might think since we're selecting "one" person, the favorable outcomes should be 1, leading to \(\frac{1}{45}\).

This may lead them to select Choice A (\(\frac{1}{45}\))

The Bottom Line:

This problem tests whether students can correctly identify what constitutes "favorable" in a probability context - it's about the desired characteristic (plays saxophone), not about how many people are selected.