A) \[\frac{3}{4}\]
B) \[\frac{1}{2}\]
C) \[\frac{2}{3}\]
D) \[\frac{1}{3}\]
Correct Answer: A
Solution :
\[P({{E}_{1}})=\frac{1}{2},{{P}_{2}}({{E}_{2}})=\frac{1}{3}\]and \[P({{E}_{3}})=\frac{1}{4}\] \[P({{E}_{1}}\cup {{E}_{1}}\cup {{E}_{3}})=1-P({{\overline{E}}_{1}})P({{\overline{E}}_{2}})P({{\overline{E}}_{3}})\] \[=1-\left( 1-\frac{1}{2} \right)\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)\] \[=1-\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}=\frac{3}{4}\]
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