A) \[\frac{^{2n}{{C}_{n}}}{{{2}^{2n}}}\]
B) \[\frac{1}{^{2n}{{C}_{n}}}\]
C) \[\frac{1\cdot 3\cdot 5...(2n+1)}{{{2}^{n}}n!}\]
D) \[\frac{{{3}^{n}}}{{{4}^{n}}}\]
Correct Answer: A
Solution :
[a] Required probability \[=\frac{\sum\limits_{r=0}^{n}{^{n}{{C}_{r}}{{\times }^{n}}{{C}_{r}}}}{{{2}^{n}}\times {{2}^{n}}}\] \[=\frac{C_{0}^{2}+C_{1}^{2}+C_{2}^{2}+...+C_{n}^{2}}{{{4}^{n}}}=\frac{^{2n}{{C}_{n}}}{{{2}^{2n}}}\]
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