MHT CET · Maths · Probability
A family with three children is chose at random. The probability that the oldest and youngest children are of the same gender is
- A \(\frac{3}{8}\)
- B \(\frac{1}{2}\)
- C \(\frac{1}{8}\)
- D \(\frac{2}{8}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{S}=\{\mathrm{BBB}, \mathrm{BBG}, \mathrm{BGB}, \mathrm{BGG}, \mathrm{GBB}, \mathrm{GBG}, \mathrm{GGB}, \mathrm{GGG}\}\)
\(\mathrm{E}=\{\mathrm{BBB}, \mathrm{BGB}, \mathrm{GBG}, \mathrm{GGG}\}\)
\(P(\mathrm{E})=\frac{n(\mathrm{E})}{n(\mathrm{~S})}=\frac{4}{8}=\frac{1}{2}\)
\(\mathrm{E}=\{\mathrm{BBB}, \mathrm{BGB}, \mathrm{GBG}, \mathrm{GGG}\}\)
\(P(\mathrm{E})=\frac{n(\mathrm{E})}{n(\mathrm{~S})}=\frac{4}{8}=\frac{1}{2}\)
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