Q76 / 150 · MHT CET 2022 (07 Aug Shift 2) · Mathematics

A family with three children is chose at random. The probability that the oldest and youngest children are of the same gender is

  • A
    $\frac{3}{8}$
  • Correct answer
    B
    $\frac{1}{2}$
  • C
    $\frac{1}{8}$
  • D
    $\frac{2}{8}$

Solution

$\mathrm{S}=\{\mathrm{BBB}, \mathrm{BBG}, \mathrm{BGB}, \mathrm{BGG}, \mathrm{GBB}, \mathrm{GBG}, \mathrm{GGB}, \mathrm{GGG}\}$ $\mathrm{E}=\{\mathrm{BBB}, \mathrm{BGB}, \mathrm{GBG}, \mathrm{GGG}\}$ $P(\mathrm{E})=\frac{n(\mathrm{E})}{n(\mathrm{~S})}=\frac{4}{8}=\frac{1}{2}$

Hence, the correct answer is option: 'B'.

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