Let [math]b(2n,.5,n)[/math] be the probability that in [math]2n[/math] tosses of a fair coin exactly [math]n[/math] heads turn up. Using Stirling's formula (Theorem), show that [math]b(2n,.5,n)\sim 1/\sqrt{\pi n}[/math]. Use the program BinomialProbabilities to compare this with the exact value for [math]n = 10[/math] to 25.