A) 3
B) 4
C) 5
D) None of these
Correct Answer: C
Solution :
[c] Let \[{{E}_{1}}\]denote the event ??a coin with head on both sides is selected? and \[{{E}_{2}}\] denotes the event?? a fair coin is selected?? Let A be the event ??he toss, results in heads??. \[\therefore P({{E}_{1}})=\frac{1}{n+1},P({{E}_{2}})=\frac{n}{n+1}\] and \[P\left( \frac{A}{{{E}_{1}}} \right)=1,P\left( \frac{A}{{{E}_{2}}} \right)=\frac{1}{2}\] \[\therefore P(A)=P({{E}_{1}})P\left( \frac{A}{{{E}_{1}}} \right)+P({{E}_{2}})P\left( \frac{A}{{{E}_{2}}} \right)\] \[\Rightarrow \frac{7}{12}=\frac{1}{n+1}\times 1+\frac{n}{n+1}\times \frac{1}{2}\Rightarrow n=5\]
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