No; your distribution gives probabilities [0.253247, 0.168831, 0.155844, 0.168831, 0.253247] for the number of Rs in the first four trials. This predicts that the number of experiments with two Rs is binomially (i.e. approximately normally) distributed with mean ~155844 and standard deviation ~363, but the actual number is 161832, around 16 standard deviations away from the mean.
The Bernoulli rate is drawn according to
Beta(0.6,0.6)
giving posterior
k+0.65.2.
No; your distribution gives probabilities [0.253247, 0.168831, 0.155844, 0.168831, 0.253247] for the number of Rs in the first four trials. This predicts that the number of experiments with two Rs is binomially (i.e. approximately normally) distributed with mean ~155844 and standard deviation ~363, but the actual number is 161832, around 16 standard deviations away from the mean.