The binomial distribution has the interesting property that it is skewed for probabilities unequal. For me as a decision scientists this means that if $100$ individuals repeat the same bernoulli experiment $10$ times, then the majority of individuals will (on average) see the event less often than expected if $p < .5$ and more often than expected if $p > .5$.
This has fundamental implications for how we (as humans, organizations, etc.) behave in environments with rare events. Namely we can expect that the majority of individuals will be thinking that the rare event is less likely than expected (provided we are in a world governed by the binomial distribution). Now the question is can this reasoning be extended beyond the binomial-distribution-world? For instance, if one was to binarize a multinomial distribution into the probability of one event versus the rest, would the resulting distribution also be skewed (when viewed as a function of the events probability)? Or, if we sample from a normal distribution, and we ask whether individuals see events more extreme than 3SD (on average) more often than their to their expectation (i.e., their relativ mass in the distribution) or less often.