probability of a 50/50 event occurring 15/20 times divided by the probability of a 75/25 event occurring 15/20 times

Question

The material I am working with:

http://personal.vu.nl/a.f.de.vos/primer/primer.pdf

Article describes probability of a 50/50 event occurring 15/20 times divided by the probability of a 75/25 event occurring 15/20 times as being equal to 1/13.7% or 7.2992%

I am getting 7.3077%

Is this a rounding issue or am I offtrack? You can see my attempt at calculating the binomial distribution below

Answer 1

The probability that an event with probability $p$ will occur exactly $15$ times out of $20$ is $${20\choose15}p^{15}(1-p)^5$$ Therefore, the quotient you seek is $${.5^{20}\over .75^{15}.25^5}\approx.073077$$ and I think you are correct.