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Question: Answered & Verified by Expert
A committee of two persons is selected from two men and two women. The probability that the committee will have exactly one woman is
MathematicsProbabilityNDANDA 2017 (Phase 2)
Options:
  • A $\frac{1}{6}$
  • B $\frac{2}{3}$
  • C $\frac{1}{3}$
  • D $\frac{1}{2}$
Solution:
1117 Upvotes Verified Answer
The correct answer is: $\frac{2}{3}$
We know, $\mathrm{P}(\mathrm{E})=\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }}$
Number of possible outcomes $={ }^{4} \mathrm{C}_{2}=\frac{4 \times 3}{2 \times 1}=6$
(selecting 2 people from 4 people $)$ Number of favourable outcomes
$={ }^{2} \mathrm{C}_{1} \times{ }^{2} \mathrm{C}_{1}=2 \times 2=4$
(selecting 1 from 2 men, 1 from 2 women)
$\mathrm{P}(\mathrm{E})=\frac{4}{6}=\frac{2}{3}$

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