Q251 / 270 · NDA 2024 (Phase 1) · Mathematics

A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?

  • A
    $\frac{1}{6}$
  • B
    $\frac{5}{108}$
  • Correct answer
    C
    $\frac{4}{9}$
  • D
    $\frac{5}{18}$

Solution

Required probability $\begin{aligned} p(\mathrm{E}) & =\frac{{ }^5 \mathrm{C}_2+{ }^4 \mathrm{C}_2}{{ }^9 \mathrm{C}_2}=\frac{\frac{5 \times 4}{2}+\frac{4 \times 3}{2}}{\frac{9 \times 8}{2}} \\ & =\frac{10+6}{36}=\frac{16}{36}=\frac{4}{9} \end{aligned}$

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

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