Problem-Solving and Data AnalysisHardProbability of two dependent draws
Problem-Solving and Data Analysis practice question
A drawer holds 5 socks: 2 black and 3 white. Two socks are taken out at random one after the other without replacement. What is the probability that both are black?
Answer: 1/10 or 0.1
First black: 2/5. Then 1 black of 4 remain: 1/4. Product: 2/5 × 1/4 = 1/10.
Common wrong answers
- If you answered 4/25
- 4/25 is (2/5)², which assumes the first sock is put back.
- If you answered 1/5
- 1/5 uses 1/2 for the second draw; only 1 black sock remains among 4.
- If you answered 2/5
- 2/5 is the probability that the FIRST sock is black.
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