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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Probability

NDA 2010 · Mathematics · Probability

Two balls are selected from a box containing 2 blue and 7 red...

Two balls are selected from a box containing 2 blue and 7 red balls. What is the probability that at least one ball is blue?

Options

  1. A29\frac{2}{9}
  2. B79\frac{7}{9}
  3. C512\frac{5}{12}
  4. D712\frac{7}{12}

Correct answer

D. 712\frac{7}{12}

Step-by-step solution

P=2C1×7C19C2+2C2×7C09C2=2×736+1×736=14+736=712\begin{aligned} & \mathrm{P}=\frac{{ }^2 \mathrm{C}_1 \times{ }^7 \mathrm{C}_1}{{ }^9 \mathrm{C}_2}+\frac{{ }^2 \mathrm{C}_2 \times{ }^7 \mathrm{C}_0}{{ }^9 \mathrm{C}_2} \\ & =\frac{2 \times 7}{36}+\frac{1 \times 7}{36}=\frac{14+7}{36}=\frac{7}{12}\end{aligned}
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