A) \[\frac{1}{2}\]
B) \[\frac{1}{12}\]
C) \[\frac{1}{4}\]
D) None of these
Correct Answer: A
Solution :
Let\[{{E}_{1}}\]be the events that man will be selected and\[{{E}_{2}}\]the events that woman will be selected Then, \[P({{E}_{1}})=\frac{1}{4}\] So, \[P({{\bar{E}}_{1}})=1-\frac{1}{4}=\frac{3}{4}\] and \[P({{E}_{2}})=\frac{1}{3}\] \[\Rightarrow \] \[P({{\bar{E}}_{2}})=\frac{2}{3}\] \[\therefore \]\[{{E}_{1}}\]and\[{{E}_{2}}\]are independent events. \[P({{\bar{E}}_{1}}\cap {{\bar{E}}_{2}})=P({{\bar{E}}_{1}})\times P({{\bar{E}}_{2}})\] \[=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}\]
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