For a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. A bead...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
For a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?
1. TRANSLATE the problem information
- Given information:
- 29 out of every 100 beads have a defect
- One bead will be selected at random
- This tells us we have a ratio: 29 defective beads for every 100 total beads
2. INFER the approach
- This is asking for probability of a specific outcome
- Use the probability formula: \(\mathrm{P = \frac{favorable\,outcomes}{total\,outcomes}}\)
- Favorable outcome = selecting a defective bead
- Total outcomes = all possible beads that could be selected
3. Set up the probability calculation
- Favorable outcomes = 29 (defective beads)
- Total outcomes = 100 (total beads)
- Therefore: \(\mathrm{P(defective\,bead) = \frac{29}{100}}\)
Answer: C. \(\mathrm{\frac{29}{100}}\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret "29 out of 100" and create the wrong fraction setup.
Some students might think they need to find "the probability that it's NOT 29 out of 100" and calculate something like \(\mathrm{\frac{1}{29}}\), or they might get confused about which number goes in the numerator versus denominator. Others might incorrectly multiply the numbers together, leading to calculations involving 2,900.
This may lead them to select Choice A (\(\mathrm{\frac{1}{2,900}}\)) or Choice B (\(\mathrm{\frac{1}{29}}\)).
Second Most Common Error:
Poor TRANSLATE reasoning: Students correctly understand it's 29 defective beads but misunderstand what "out of 100" means in the context of probability.
They might think "out of 100" means they should use 10 as the denominator instead of 100, leading them to write \(\mathrm{\frac{29}{10}}\).
This may lead them to select Choice D (\(\mathrm{\frac{29}{10}}\)).
The Bottom Line:
This problem tests whether students understand that probability is simply the ratio of favorable outcomes to total outcomes. The key insight is recognizing that "29 out of every 100" directly gives you both the numerator and denominator for the probability fraction.