Voice typeNumber of singersCountertenor4Tenor6Baritone10Bass5A total of 25 men registered for singing lessons. The frequency table shows how many of t...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
| Voice type | Number of singers |
|---|---|
| Countertenor | 4 |
| Tenor | 6 |
| Baritone | 10 |
| Bass | 5 |
A total of 25 men registered for singing lessons. The frequency table shows how many of these singers have certain voice types. If one of these singers is selected at random, what is the probability he is a baritone?
1. TRANSLATE the problem information
- Given information:
- Frequency table showing voice types and number of singers
- Total of 25 men registered
- Need to find probability of selecting a baritone
- What this tells us: We need \(\mathrm{P(baritone)} = \frac{\text{number of baritones}}{\text{total singers}}\)
2. INFER the approach
- This is a basic probability problem using the fundamental formula
- Strategy: Count the baritones from the table, divide by total number of singers
3. SIMPLIFY to get the final answer
- From the table: Number of baritones = 10
- Total number of singers = 25
- \(\mathrm{P(baritone)} = \frac{10}{25} = 0.40\)
Answer: B. 0.40
Why Students Usually Falter on This Problem
Most Common Error Path:
Poor TRANSLATE reasoning: Students find the probability of NOT being a baritone instead of being a baritone.
They count all the non-baritone singers \(4 + 6 + 5 = 15\) and calculate \(\frac{15}{25} = 0.60\).
This may lead them to select Choice C (0.60)
Second Most Common Error:
Weak SIMPLIFY execution: Students misread the total number of singers or make arithmetic errors.
Some students might assume there are 100 total singers instead of 25, leading to \(\frac{10}{100} = 0.10\).
This may lead them to select Choice A (0.10)
The Bottom Line:
This problem tests whether students can correctly identify what they're calculating in a probability context and avoid the common trap of finding the complement probability instead.