Problem-Solving and Data AnalysisVery hardCount from a probability with an unknown
Problem-Solving and Data Analysis practice question
A bag contains r red marbles and 8 blue marbles. If the probability of drawing a red marble at random is 1/3, what is the value of r?
Answer: 4
r/(r + 8) = 1/3. Cross-multiply: 3r = r + 8, so 2r = 8 and r = 4. Check: 4/12 = 1/3.
Common wrong answers
- If you answered 8
- 8 would make red and blue equal, giving a probability of 1/2.
- If you answered 16
- 16 comes from r = 2 × 8, which gives 16/24 = 2/3 — the probability of red would be too high.
- If you answered 2.67
- 2.67 is 8/3, treating 8 as the total number of marbles; the total is r + 8.
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