For a science project, Anka recorded whether it rained each weekday and weekend day for 12 weeks. Her results are...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
For a science project, Anka recorded whether it rained each weekday and weekend day for 12 weeks. Her results are summarized in the table below.
Weekday and Weekend Day Rain for 12 Weeks| Rain | No rain | Total | |
|---|---|---|---|
| Number of weekdays | 12 | 48 | 60 |
| Number of weekend days | 8 | 16 | 24 |
| Total | 20 | 64 | 84 |
If one of the days on which there was no rain is selected at random, what is the probability the day was a weekend day?
1. TRANSLATE the problem information
- Given information from the table:
- Total days with no rain: 64
- Weekend days with no rain: 16
- Weekdays with no rain: 48
- What the question asks: "If one of the days on which there was no rain is selected at random, what is the probability the day was a weekend day?"
2. INFER the approach
- This is conditional probability - we're only selecting from days with no rain
- Our sample space is the 64 no-rain days, not all 84 days
- We need: \(\mathrm{P(weekend\,day\,|\,no\,rain\,day)} = \frac{\mathrm{weekend\,days\,with\,no\,rain}}{\mathrm{total\,no-rain\,days}}\)
3. Calculate the probability
- Favorable outcomes: 16 weekend days with no rain
- Total possible outcomes: 64 days with no rain
- Probability = \(\frac{16}{64} = \frac{1}{4}\)
Answer: B. 1/4
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Misunderstanding the sample space and calculating P(weekend day with no rain) from all 84 days instead of from just the 64 no-rain days.
Students might calculate \(\frac{16}{84} = \frac{4}{21}\), thinking they need the probability of selecting a no-rain weekend day from all possible days.
This leads them to select Choice A (4/21)
Second Most Common Error:
Poor INFER reasoning about conditional probability: Getting the condition backwards and calculating the probability that a weekend day has no rain instead of the probability that a no-rain day is a weekend day.
Students might calculate \(\frac{16}{24} = \frac{2}{3}\), finding the probability that a randomly selected weekend day had no rain.
This leads them to select Choice C (2/3)
The Bottom Line:
The key challenge is recognizing that "selected from the days with no rain" creates a restricted sample space - you're not selecting from all days, just from the 64 no-rain days. This conditional probability setup trips up many students who default to using the full dataset.