A) \[\frac{1}{2}\]
B) \[\frac{1}{6}\]
C) \[\frac{5}{8}\]
D) \[\frac{7}{8}\]
Correct Answer: A
Solution :
Probability of getting head in one trial, \[p=1/2\] and probability of not getting head, \[q=1/2\] Probability of getting head odd times \[{{=}^{20}}{{C}_{1}}{{\left( \frac{1}{2} \right)}^{1}}{{\left( \frac{1}{2} \right)}^{19}}{{+}^{20}}{{C}_{3}}{{\left( \frac{1}{2} \right)}^{3}}{{\left( \frac{1}{2} \right)}^{17}}\] \[+....{{+}^{20}}{{C}_{19}}{{\left( \frac{1}{2} \right)}^{19}}{{\left( \frac{1}{2} \right)}^{1}}\] \[=\frac{1}{{{2}^{20}}}{{[}^{20}}{{C}_{1}}{{+}^{20}}{{C}_{3}}+...{{+}^{20}}{{C}_{19}}]\] \[=\frac{1}{{{2}^{20}}}\times {{2}^{20-1}}\frac{{{2}^{19}}}{{{2}^{20}}}=\frac{1}{2}\]
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