This scenario assumes that Mother Nature is using a uniform probability distribution to select the critical story, call it C, observing that 1<=C<=H+1. Hence, the probability that C=h is equal to 1/(1+H) for h in {1,...,H+1}.

Under this convention the critical story C is the highest safe story: eggs dropped from this story (and from storiwes below it) will not break. Eggs dropped from stories above it will break.

According to the above, the probability that an egg will break when dropped from story h is equal to h/(1+H). The probability that an egg will not break when dropped from story h is therefore equal to 1-h/(1+H)=(H-h+1)/(1+H). In particular, the probability that an egg will not break when dropped from story H is equal to 1/(1+H).

It is assumed that we are attempting to minimize the expected value of the total number of egg-droppings required to identify the critical story.

Because the computation of the expected value of total number of egg-dropping inevitably produce fractions, all the arithmetic operations are carried out and reported on, using proper fractions.