  In this paper, we investigate the algebraic properties of the expectation
semirings which are semiring version of the concept of trivial extension in
ring theory. We discuss ideals, primes, maximals and primary ideals of these
semirings. We also discuss the distinguished elements such as the units,
idempotents, and zero-divisors of the expectations semirings. Similar to their
counterparts in ring theory, we introduce pr\'{e}simplifiable, domainlike,
clean, almost clean, and weakly clean semiring and see when an expectation
semiring is one of these semirings.
