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  • A bag contains 6 white and 4 black balls. $A$ dee is rolled once and the number of ball equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls

A bag contains 6 white and 4 black balls. $A$ dee is rolled once and the number of ball equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is

Option: 1

\frac{1}{4}


Option: 2

\frac{9}{50}


Option: 3

\frac{11}{50}


Option: 4

\frac{1}{5}


Answers (1)

 

\begin{aligned} & \frac{1}{6} \times\left[\frac{{ }^6 \mathrm{C}_1}{{ }^{10} \mathrm{C}_1}+\frac{{ }^6 \mathrm{C}_2}{{ }^{10} \mathrm{C}_2}+\frac{{ }^6 \mathrm{C}_3}{{ }^{10} \mathrm{C}_3}+\frac{{ }^6 \mathrm{C}_4}{{ }^{10} \mathrm{C}_4}+\frac{{ }^6 \mathrm{C}_5}{{ }^{10} \mathrm{C}_5}+\frac{{ }^6 \mathrm{C}_6}{{ }^{10} \mathrm{C}_6}\right] \\ & =\frac{1}{6}\left(\frac{126+70+35+15+5+1}{210}\right)=\frac{42}{210}=\frac{1}{5} \end{aligned}

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Kshitij

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