At a movie theater, there are a total of 350 customers. Each customer is located in either theater A, theater...

1. TRANSLATE the problem information

• Given information:
  • Total customers: 350
  • Probability of selecting from Theater A: 0.48
  • Probability of selecting from Theater B: 0.24
  • All customers are in exactly one of three theaters (A, B, or C)

• What this tells us: We can find the actual number of customers by multiplying each probability by the total.

2. INFER the solution strategy

• Since we know the total and can calculate customers in theaters A and B, we can find Theater C by subtraction
• This works because every customer must be in exactly one theater

3. SIMPLIFY to find customers in Theater A

• Number in Theater A = \(0.48 \times 350 = 168\) customers

4. SIMPLIFY to find customers in Theater B

• Number in Theater B = \(0.24 \times 350 = 84\) customers

5. SIMPLIFY to find customers in Theater C

• Customers in A and B combined: \(168 + 84 = 252\)
• Customers in Theater C: \(350 - 252 = 98\)

Answer: D. 98

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students confuse the probability of Theater C with the number of customers in Theater C.

They correctly determine that \(\mathrm{P(Theater\ C)} = 1 - 0.48 - 0.24 = 0.28\), but then think this means 28 customers are in Theater C instead of recognizing that 0.28 represents 28% of the total customers.

This leads them to select Choice A (28).

Second Most Common Error:

Poor SIMPLIFY execution: Students make calculation errors, particularly when multiplying decimals by large numbers.

Common mistakes include:

• Calculating \(0.48 \times 350 = 148\) instead of 168
• Getting confused with the subtraction: \(350 - 168 - 84\)

These arithmetic errors can lead to various incorrect answers, causing them to select Choice B (40) or get confused and guess.

Third Most Common Error:

Inadequate comprehension during problem solving: Students correctly calculate that Theater B has 84 customers but then select this as their final answer without recognizing the question asks for Theater C.

This leads them to select Choice C (84).

The Bottom Line:

This problem tests whether students can bridge the gap between probability (a ratio) and actual counts (concrete numbers), while maintaining careful attention to what the question is actually asking for.