MCQ
A bag contains $2$ white and $4$ black balls. A ball is drawn $5$ times with replacement. The probability that at least $4$ of the balls drawn are white is
- A$\frac{8}{{141}}$
- B$\frac{{10}}{{243}}$
- ✓$\frac{{11}}{{243}}$
- D$\frac{8}{{41}}$
Probability for black ball $ = \frac{4}{6} = \frac{2}{3}$
$\therefore $ Required probability
$ = {\,^5}{C_5}{\left( {\frac{1}{3}} \right)^5}\,{\left( {\frac{2}{3}} \right)^0}\, + {\,^5}{C_4}{\left( {\frac{1}{3}} \right)^4}\left( {\frac{2}{3}} \right)$
$ = {\left( {\frac{1}{3}} \right)^4}\,\left[ {\frac{1}{3} + 5.\,\frac{2}{3}} \right]$$ = \frac{{11}}{{{3^5}}} = \frac{{11}}{{243}}$.
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