The table summarizes the distribution of age and assigned group for 90 participants in a study.0-9 years10-19 years20+ yearsTotalGroup A517830Group...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The table summarizes the distribution of age and assigned group for 90 participants in a study.
| 0-9 years | 10-19 years | 20+ years | Total | |
|---|---|---|---|---|
| Group A | 5 | 17 | 8 | 30 |
| Group B | 6 | 8 | 16 | 30 |
| Group C | 19 | 5 | 6 | 30 |
| Total | 30 | 30 | 30 | 90 |
One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10 years of age?
\(\frac{5}{18}\)
\(\frac{5}{12}\)
\(\frac{17}{30}\)
\(\frac{5}{6}\)
1. TRANSLATE the problem information
- Given information:
- Table showing 90 participants by age group and study group
- Need probability of Group A selection, given age ≥ 10 years
- This translates to: \(\mathrm{P(Group\,A\,|\,Age\,\geq\,10)}\)
2. INFER the conditional probability approach
- Key insight: The condition "at least 10 years of age" restricts our sample space
- We only consider participants who meet the age condition (≥ 10 years)
- Formula: \(\mathrm{P(Group\,A\,|\,Age\,\geq\,10)\,=\,\frac{Group\,A\,participants\,\geq\,10}{Total\,participants\,\geq\,10}}\)
3. Count Group A participants who are at least 10 years old
- From table: Group A has 17 participants (age 10-19) + 8 participants (age 20+)
- Group A participants ≥ 10: \(\mathrm{17 + 8 = 25}\)
4. Count total participants who are at least 10 years old
- From table: 30 participants (age 10-19) + 30 participants (age 20+)
- Total participants ≥ 10: \(\mathrm{30 + 30 = 60}\)
5. SIMPLIFY the probability calculation
- \(\mathrm{P(Group\,A\,|\,Age\,\geq\,10)\,=\,\frac{25}{60}}\)
- SIMPLIFY by dividing both numerator and denominator by 5: \(\mathrm{\frac{25}{60}\,=\,\frac{5}{12}}\)
Answer: B. 5/12
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students miss that the condition restricts the sample space and use all 90 participants as the denominator instead of just the 60 who are ≥ 10 years old.
They calculate: \(\mathrm{\frac{25}{90}\,=\,\frac{5}{18}}\)
This may lead them to select Choice A (5/18)
Second Most Common Error:
Poor TRANSLATE reasoning: Students misinterpret "at least 10 years of age" to mean only the 10-19 age group, missing the 20+ group.
They calculate: \(\mathrm{\frac{17}{30}}\) (only using 10-19 year olds in Group A over total 10-19 year olds)
This may lead them to select Choice C (17/30)
The Bottom Line:
Conditional probability problems require careful attention to how the given condition restricts the sample space. The key insight is recognizing that "given age ≥ 10" means we're only working with that subset of participants, not the entire population.
\(\frac{5}{18}\)
\(\frac{5}{12}\)
\(\frac{17}{30}\)
\(\frac{5}{6}\)