A) \[\frac{4}{27}\]
B) \[\frac{8}{27}\]
C) \[\frac{16}{27}\]
D) \[\frac{24}{27}\]
Correct Answer: C
Solution :
Probability of failure = \[\frac{1}{3}\] Probability for getting success \[=\frac{2}{3}\] \ Required probability \[={{\,}^{4}}{{C}_{4}}{{\left( \frac{2}{3} \right)}^{4}}{{\left( \frac{1}{3} \right)}^{0}}+{{\,}^{4}}{{C}_{3}}{{\left( \frac{2}{3} \right)}^{3}}\left( \frac{1}{3} \right)\] \[={{\left( \frac{2}{3} \right)}^{4}}+4{{\left( \frac{2}{3} \right)}^{3}}\left( \frac{1}{3} \right)=\frac{16}{27}\].
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