Problem-Solving and Data AnalysisHardTwo draws without replacement
Problem-Solving and Data Analysis practice question
A bag contains 3 red marbles and 2 blue marbles. Two marbles are drawn at random, one after the other, WITHOUT replacement. What is the probability that both are red?
- A. 3/10Correct
- B. 9/25
- C. 3/5
- D. 1/5
Answer: A. 3/10
First draw: 3/5 red. Then 2 red remain among 4: 2/4. Multiply: (3/5)(2/4) = 6/20 = 3/10.
Why the other answers are wrong
- B. 9/25
- 9/25 is (3/5)(3/5), the probability WITH replacement.
- C. 3/5
- 3/5 is the probability of red on the first draw only.
- D. 1/5
- 1/5 is (3/5)(1/3) or a similar slip; after one red is drawn, 2 of the remaining 4 are red, so the second factor is 2/4.
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