A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. Then, the probability that…

A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. Then, the probability that none of the balls drawn is blue is
  1. $10 / 21$
  2. $11 / 21$
  3. $2 / 7$
  4. $5 / 7$

Solution

Given bag contains 2 red, 3 green 2 blue balls $ \begin{aligned} & \mathrm{P} \text { (none ball drawn is blue) }=\frac{{ }^2 \mathrm{c}_2+{ }^3 \mathrm{c}_2+{ }^2 \mathrm{c}_1+{ }^3 \mathrm{c}_1}{{ }^7 \mathrm{c}_2} \\ & =\frac{1+3+2 \times 3}{\frac{7 \times 6}{2}}=\frac{4+6}{7 \times 3}=\frac{10}{21} \end{aligned} $

Asked in: AP EAMCET 2022 (06 Jul Shift 1)

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