Q76 / 160 · TS EAMCET 2022 (19 Jul Shift 2) · Mathematics

A bag contains 3 white and 6 red balls. Four balls are drawn at a time randomly. Then the probability of getting at least red balls is

  • A
    $\frac{8}{27}$
  • B
    $\frac{5}{14}$
  • Correct answer
    C
    $\frac{60}{63}$
  • D
    $\frac{1}{2}$

Solution

We have, $\mathrm{W}=3, \mathrm{R}=6$ Now probability of getting at least two red balls $$ \begin{aligned} & =\frac{{ }^6 \mathrm{C}_2 \times{ }^3 \mathrm{C}_2+{ }^6 \mathrm{C}_3 \times{ }^3 \mathrm{C}_1+{ }^6 \mathrm{C}_4}{{ }^9 \mathrm{C}_4} \\ & \frac{60}{63} \text { or } \frac{20}{21} \end{aligned} $$

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

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