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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Probability

NDA 2024 · Mathematics · Probability

A bag contains 5 black and 4 white balls. A man selects two balls...

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?

Options

  1. A16\frac{1}{6}
  2. B5108\frac{5}{108}
  3. C49\frac{4}{9}
  4. D518\frac{5}{18}

Correct answer

C. 49\frac{4}{9}

Step-by-step solution

Required probability p(E)=5C2+4C29C2=5×42+4×329×82=10+636=1636=49\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}
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