# start with N = number of repetitions, n = number of courses
# also start with pa = Pr(A), pb = Pr(B), pc = Pr(C)
#
grpts = rep(NA, times = n)
GPA = rep(NA, times = N)
GPmax = rep(NA, times = N)
for (i in 1:N) {
   rand = runif(n,0,1)
   for (j in 1:n) {
      if (rand[j] < pa) {grpts[j] = 4}
      if ((rand[j] >= pa) & (rand[j] < pa+pb)) {grpts[j] = 3}
      if (rand[j] >= pa+pb) {grpts[j] = 2}
   }
   GPA[i] = mean(grpts)
   GPmax[i] = max(grpts)
}
hist(GPmax); table(GPmax)
mean(GPmax); sd(GPmax)
hist(GPA); table(GPA)
mean(GPA); sd(GPA)