A) \[\frac{1}{64}\]
B) \[\frac{3}{16}\]
C) \[\frac{1}{2}\]
D) \[\frac{13}{16}\]
Correct Answer: D
Solution :
[d] \[P{{=}^{5}}{{C}_{2}}{{\left( \frac{1}{2} \right)}^{2}}{{\left( \frac{1}{2} \right)}^{3}}{{+}^{5}}{{C}_{3}}{{\left( \frac{1}{2} \right)}^{3}}{{\left( \frac{1}{2} \right)}^{3}}\] \[{{+}^{5}}{{C}_{4}}{{\left( \frac{1}{2} \right)}^{4}}{{\left( \frac{1}{2} \right)}^{1}}{{+}^{5}}{{C}_{2}}{{\left( \frac{1}{2} \right)}^{5}}{{\left( \frac{1}{2} \right)}^{0}}\] \[={{\left( \frac{1}{2} \right)}^{5}}\left[ ^{5}{{C}_{2}}{{+}^{5}}{{C}_{3}}{{+}^{5}}{{C}_{4}}{{+}^{5}}{{C}_{5}} \right]\] \[=\frac{1}{{{3}^{2}}}\times 26=\frac{13}{16}.\]
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