Wikipedia gives the intuitive meaning of the expected value as
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the same experiment it represents
It seems that the "long-run average value of repetitions" should be likely to occur in an experiment. I would expect $P(X=E(X))$ to be very high. After all, if a value is the long-run average value of repetitions, then it seems to occur frequently.
However, for example, $X \sim B(n=20, p=0.05)$. $E(X) = 1$, but $P(X=1) = 0.377$.
Why is "the long-run average value of repetitions" not likely to occur in an experiment?