The Cohenian paradox is one of the main themes of judicial probability theory and one of the core topics discussed by the new evidence scholarship. To resolve this paradox, evidence scholars nowadays have proposed various solutions, including legal probabilism, Bayesian decision theory, and relative plausibility theory. These three solutions can be classified into two approaches, i.e., the probabilism and the explanationism. Among them, the former includes legal probabilism and Bayesian decision theory, and the latter includes the relative plausibility theory. However, the two approaches have recently begun to converge and become more understandable to each other. For example, Welch (2020) has recently defended and improved the relative plausibility theory by substantially improving it with the help of Bayesian decision theory. In this paper, by contrast, we attempt to defend the probabilistic approach - legal probabilism and Bayesian decision theory on the basis of relative plausibility theory.