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Question: Answered & Verified by Expert
A box contains 10 identical electronic components of which 4 are defective. If 3 components are selected at random from the box in succession, without replacing the units already drawn, what is the probability that two of the selected components are defective?
MathematicsProbabilityNDANDA 2007 (Phase 1)
Options:
  • A $1 / 5$
  • B $5 / 24$
  • C $3 / 10$
  • D $1 / 40$
Solution:
1438 Upvotes Verified Answer
The correct answer is: $3 / 10$
Total number of selecting 3 components out of $10=$ ${ }^{10} \mathrm{C}_{3}$. Out of 3 selected components two defective pieces can be selected in ${ }^{4} \mathrm{C}_{2}$ ways and one non-defective piece will be selected in ${ }^{6} \mathrm{C}_{1}$ ways, hence.
Required probability $=\frac{{ }^{6} \mathrm{C}_{1} \times{ }^{4} \mathrm{C}_{2}}{{ }^{10} \mathrm{C}_{3}}=\frac{6 \times 6 \times 6}{10 \times 9 \times 8}=\frac{3}{10}$

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