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  4. A bag contains 10 white and 3 black balls. Balls are drawn one by one without replacement till all the black balls are drawn. The probability that the procedure of drawing balls will come to an end at the 7t h draw is

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Q. A bag contains $10$ white and $3$ black balls. Balls are drawn one by one without replacement till all the black balls are drawn. The probability that the procedure of drawing balls will come to an end at the $7^{t h}$ draw is

NTA AbhyasNTA Abhyas 2020Probability

Solution:

The drawing procedure ends at $7^{t h}$ draw, if $3^{r d}$ black ball comes at $7^{t h}$ draw. Hence, in $1^{s t}$ six draws there will be $2$ black balls and $4$ white balls.

So, required Probability $=\frac{^{10}C_{4}^{} \times \_{}^{3}C_{2}^{}}{^{13}C_{6}^{}}\times \frac{1}{7}$ $=\frac{15}{286}$