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 event that man will be selected and \[{{E}_{2}}\] the event 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 \[P({{E}_{2}})=\frac{1}{3}\] So \[P({{\bar{E}}_{2}})=\frac{2}{3}\] Clearly \[{{E}_{1}}\] and \[{{E}_{2}}\] are independent events. So, \[P({{\bar{E}}_{1}}\cap {{\bar{E}}_{2}})=P({{\bar{E}}_{1}})\times P({{\bar{E}}_{2}})=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}\].
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