A) \[^{5}{{C}_{4}}{{\left( \frac{1}{3} \right)}^{4}}\left( \frac{2}{3} \right)\]
B) \[^{5}{{C}_{4}}\left( \frac{1}{3} \right){{\left( \frac{2}{3} \right)}^{4}}\]
C) \[^{5}{{C}_{4}}{{\left( \frac{1}{6} \right)}^{5}}\]
D) \[^{5}{{C}_{4}}{{\left( \frac{1}{6} \right)}^{4}}\left( \frac{5}{6} \right)\]
E) \[^{5}{{C}_{4}}{{\left( \frac{5}{6} \right)}^{4}}\left( \frac{1}{6} \right)\]
Correct Answer: A
Solution :
Probability of success,\[p=\frac{2}{6}=\frac{1}{3}\]and probability of failure, \[q=\frac{2}{3}\] \[\therefore \]Required probability\[{{=}^{5}}{{C}_{4}}{{\left( \frac{1}{4} \right)}^{4}}\left( \frac{2}{3} \right)\]
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