Wow, Ali! That truly is a tough one!

Let me recap the assumptions here:

1. Two activities on the critical path

2. Activity duration following a Beta distribution

3. Duration uncertainty (i.e., standard deviation, sigma) known for each activity.

Please notice that the description here sounds a bit misleading to me. In fact, if you assume a beta distribution, the standard deviation is sigma = (P - O)/6, where P and O are the most pessimistic and most optimistic durations, respectively. Not that we will use this formula to solve this problem, but reading it as P - O confused me in the beginning.

4. Confidence interval as +/- 3sigma. This won't be needed to solve our problem

Now, from some statistical theorems, we know that the variance of the project is equal to the sum of the variances of the activities on the critical path. In our case:

var_p = var_1 + var_2 = (sigma_1)^2 + (sigma_2)^2 = 18^2 + 24^2 = 900

So the standard deviation for the project (i.e., its duration uncertainty) is sigma_p = sqrt(var_p) = 30.

Therefore the correct answer should be option B.

That said, I've never seen anything like this in the actual exam, nor even in the exam simulations I practiced. Thanks for sharing it.

Gabriella