Prices of 14 Different Cars Type of car Priced at no more than $25,000 Priced greater than $25,000 Total Nonhybrid...

1. TRANSLATE the problem information

• Given information:
  • We have a two-way table showing 14 cars categorized by type and price
  • We want the probability of selecting a hybrid car priced at no more than \(\$25,000\)

• What this tells us: We need to find a specific intersection in the table and calculate probability using all 14 cars.

2. TRANSLATE to locate the favorable outcome

• Looking at the table, find the intersection of:
  • Row: "Hybrid"
  • Column: "Priced at no more than \(\$25,000\)"
• This cell shows: 2 cars

3. INFER the probability setup

• For probability problems with random selection:
  • Favorable outcomes = 2 (hybrid cars \(\leq \$25,000\))
  • Total possible outcomes = 14 (all cars)
• We use ALL cars in the denominator because we're selecting from all cars randomly

4. SIMPLIFY the calculation

• Probability = \(\frac{2}{14}\)

\(= \frac{1}{7}\)

Answer: A. \(\frac{1}{7}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misidentify which cell represents the desired outcome.

They might look at "Hybrid" and "Priced greater than \(\$25,000\)" instead, finding 4 cars. Using \(\frac{4}{14}\)

\(= \frac{2}{7}\), they select Choice B (\(\frac{2}{7}\)).

Second Most Common Error:

Poor INFER reasoning about probability setup: Students correctly find 2 hybrid cars \(\leq \$25,000\), but use only hybrid cars (6 total) as the denominator instead of all cars.

They calculate \(\frac{2}{6}\)

\(= \frac{1}{3}\) and select Choice C (\(\frac{1}{3}\)). This treats the problem as "given that I'm choosing a hybrid car, what's the probability it costs \(\leq \$25,000\)?" rather than the actual question.

The Bottom Line:

Two-way table probability problems require careful attention to exactly what the problem asks for AND using the correct total in the denominator. The key insight is that random selection from the entire population means the denominator should be the grand total, not a subset.