Either you get "red" or you don't. That's binomial. The probability of getting "red" is 1/2, same as the probability of getting "black."
So we have a binomial probability distribution with n=38, p=1/2 and x = 19.
Using the binompdf( function built into my TI-83 calculator, I get
binompdf(38, 1/2, 19) = 0.129 (answer)
