A) \[\frac{8}{141}\]
B) \[\frac{10}{243}\]
C) \[\frac{11}{243}\]
D) \[\frac{8}{41}\]
Correct Answer: C
Solution :
Probability for white ball \[=\frac{2}{6}=\frac{1}{3}\] 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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