Problem-Solving and Data AnalysisHardTwo draws with replacement
Problem-Solving and Data Analysis practice question
A jar contains 5 red marbles and 3 green marbles. A marble is drawn at random, replaced, and a second marble is drawn at random. What is the probability that both marbles are red?
- A. 25/64Correct
- B. 5/14
- C. 5/8
- D. 10/16
Answer: A. 25/64
With replacement, the draws are independent and each has probability 5/8 of red: (5/8)(5/8) = 25/64.
Why the other answers are wrong
- B. 5/14
- 5/14 is (5/8)(4/7), the probability WITHOUT replacement.
- C. 5/8
- 5/8 is the probability of red on ONE draw.
- D. 10/16
- 10/16 adds the two probabilities instead of multiplying them (and equals 5/8).
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