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Question: Answered & Verified by Expert
A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?
MathematicsProbabilityNDANDA 2014 (Phase 1)
Options:
  • A $2 / 5$
  • B $1 / 5$
  • C $1 / 10$
  • D None of these
Solution:
2181 Upvotes Verified Answer
The correct answer is: $1 / 5$
Total number of balls $=5$ Number of black balls $=2$ Required probability $=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{{ }^{2} \mathrm{C}_{1} \times{ }^{1} \mathrm{C}_{1}}{{ }^{5} \mathrm{C}_{2}}=\frac{2}{5} \times \frac{1}{2}=\frac{1}{5}$

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