Question

A fair coin is tossed $2n$ times, then the probability that the outcomes do not result in an equal number of heads and tails is

• A. $1-\frac{(2n)!}{(n!)^{2}}(\frac{1}{2})^{2n}$
• B. $1-\frac{(2n)!}{(n!)^{2}}$
• C. $\frac{(2n)!}{(n!)^{2}}(\frac{1}{2})^{2n}$
• D. $\frac{(2n)!}{(n!)^{2}}$

Hint:

In $2n$ tosses, the "central" term of the binomial expansion is always the most likely single outcome, but as $n$ increases, its probability $\frac{\binom{2n}{n}}{2^{2n}}$ actually approaches zero (approx. $\frac{1}{\sqrt{n\pi}}$).

Answer 1

The Correct Option is A