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