fair <- rbinom(50000, 20, .5)
sum(fair == 14)
# 1888

biased <- rbinom(50000, 20, .75)
sum(biased == 14)
# 8372

1888 + 8372
# [1] 10260

$$\Pr(\text{Biased}|\text{14 Heads})=$$ $$\frac{\text{\# biased w/14 Heads}}{\text{\# total w/14 Heads}}$$

$$=\frac{8372}{1888+8372}=82\%$$