Thanks for pointing that out…
*Revisioning on expected value chapter*

I do not believe that example works. We are interested in expected value, not the probability of different drop combinations (both, only A, only B, nothing). In the example given, we still wind up with the expected number of gems being the same under both calculations.

I can state my point from the earlier comment differently: if two functions have the same value across all points in the domain, they are the same function (despite surface differences in how they are written). I believe this is case with the two calculation methods in this post.

In the first calculation, it’ll drop either A or B is 100%, since A + B = 50%+50% = 100%
On the second calculation (Mine), that would be, 25% dropping both A and B, 25% only drop A, 25% only drop B, and 25% drop nothing.

The reason that I believe the drop rate is independent: We had report on 2 epic gem dropping on one prospect. Note that, it’s a rare case, since the chance would be (6C2) x (0.045)^2 x (0.955)^2, that would be around 2.216%.

And you second question.
the chance of dropping 6 epic gem is 9.9 * 10^6. This pose not much impact on the calculation, but the previous 2.216% is significant enough.

The reason that the two calculation more the less yield the same amount is that. the 4.5% is far from the 50%, the larger the chance, the more significant the error will be.
The purpose of this post is to remind the calculation error, so that it won’t be used on other aspect, e.g. grinding drops on mobs.

Can you come up with an example where the two calculations arrive at different answers? If not, I don’t think you can fairly call the first calculation wrong.

Also, is it possible to get all six gems from one prospect? If not, I don’t believe either calculation is correct.