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Probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSProbability1 Mark
MCQ
Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection is:
  • A
    $\frac{11}{21}$
  • B
    $\frac{9}{21}$
  • ✓
    $\frac {10}{21}$
  • D
    None of these
✓

Answer

Correct option: C.
$\frac {10}{21}$
There are nine persons (three men, two women and four children) out of which four persons can be selected in $\ ^{9}\text{C}_4 = 126\ \text{ways}.$
Total number of elementary events = 126
Exactly two children means selecting two children and two other people from three men and two women.
This can be done in $\ ^{4}\text{C}_2\times\ ^{ 5}\text{C}_2 \text{ways}.$
Favourable number of elementary events$=\ ^{4}\text{C}_2\times\ ^{ 5}\text{C}_2 = 60$
So, required probability $=\frac{60}{120} =\frac{10}{21}$

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