As I understand it, the question is: What is the probability that a class of 10 students with variable credit between 1 and 9 credits will accumulate at least 30 credits total.

As with any model, it ends up with some free parameters that can be estimated from previous experience. This model is a Markov chain model with 5 parameters.

  1. The probability of needing financial aid, \(P(FA) = 0.7\).
  2. The probability of being a full-time student given financial aid, \(P(FT | FA) = 0.6\).
  3. The probability of needing 3 units given being a full-time student and financial aid, \(P(3 | FT \wedge FA) = 0.1\).
  4. The probability of needing 6 units given being a full-time student and financial aid, \(P(6 | FT \wedge FA) = 0.15\).
  5. The probability of needing 2 units given being a part-time student and financial aid, \(P(2 | PT \wedge FA) = 0.25\).
h.probs  <- c(fa.ft.3=p.fa * p.ft.fa * p.3.ft.fa,
              fa.ft.6=p.fa * p.ft.fa * p.6.ft.fa,
              fa.ft.9=p.fa * p.ft.fa * (1 - (p.3.ft.fa + p.6.ft.fa)),
              fa.pt.3=p.fa * (1-p.ft.fa) * p.2.pt.fa,
              fa.pt.5=p.fa * (1-p.ft.fa) * (1-p.2.pt.fa),
              no.fa=1-p.fa)
h.probs
## fa.ft.3 fa.ft.6 fa.ft.9 fa.pt.3 fa.pt.5   no.fa 
##   0.042   0.063   0.315   0.070   0.210   0.300

The simulation samples 10 students with each of the above probabilities and sums their credits. It does this repeatedly to determine the long-term proportion of times the total ends up being greater than or equal to 30 credits.

tot.cred <- replicate(10000, sum(sample(c(3, 6, 9, 2, 5, 1), size = 10, replace=TRUE, prob=h.probs)))
hist(tot.cred)
abline(v=30, col="red")

plot of chunk unnamed-chunk-2

sum(tot.cred >= 30) / length(tot.cred)
## [1] 0.9684