A theoretical model for DNA computing using the recombination behavior of DNA molecules known as asplicing system has been introduced in 1987. Splicing systems are based on the splicing operation which, informally, cuts two strings at the specific places and attaches the prefix of the first string to the suffix of the second string and the prefix of the second string to the suffix of the first string yielding the new strings. It is known that splicing systems with finite sets of axioms and splicing rules only generate regular languages. Hence, different types of restrictions for splicing systems have been considered to increase the computational power of the languages generated. Recently, probabilistic splicing systems have been introduced where the probabilities are initially associated with the axioms, and the probabilities of the generated strings are computed from the probabilities of the initial strings. In this paper, some properties of probabilistic one-sided splicing systems, which are special types of probabilistic splicing systems, are investigated. We prove that probabilistic one-sided splicing systems can also increase the computational power of the languages generated.