A) \[\frac{35}{{{2}^{12}}}\]
B) \[\frac{35}{{{2}^{14}}}\]
C) \[\frac{7}{{{2}^{12}}}\]
D) None of these
Correct Answer: A
Solution :
Let the coin be tossed \[n\] times \[P\](7 heads) \[={}^{n}{{C}_{7}}{{\left( \frac{1}{2} \right)}^{7}}{{\left( \frac{1}{2} \right)}^{n-7}}={}^{n}{{C}_{7}}{{\left( \frac{1}{2} \right)}^{n}}\] and \[P\](9 heads) \[={}^{n}{{C}_{9}}{{\left( \frac{1}{2} \right)}^{9}}{{\left( \frac{1}{2} \right)}^{n-9}}={}^{n}{{C}_{9}}{{\left( \frac{1}{2} \right)}^{n}}\] \[P\](7 heads) \[=P\](9 heads) \[\Rightarrow {}^{n}{{C}_{7}}={}^{n}{{C}_{9}}\Rightarrow n=16\] \[\therefore \,\,\,P\](3 heads) \[={}^{16}{{C}_{3}}{{\left( \frac{1}{2} \right)}^{3}}{{\left( \frac{1}{2} \right)}^{16-3}}={}^{16}{{C}_{3}}{{\left( \frac{1}{2} \right)}^{16}}=\frac{35}{{{2}^{12}}}.\]
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