Eradicating poliomyelitis has been a major health concern to stakeholders the world over. In this study, we have developed a pair of stochastic equations for the extinction probability functions in two types of human transmission agents namely: infectives (types 1) and carriers (type 2). By solving the equations, the result shows that with only one asymptomatic carrier in a population, eradication is possible when (ß₂₂+ß₂₁+µ)²>4ß₂₂µ where ß_ij is the Poisson rate at which type i transmission agent produces type j transmission agent and µ is the mean infectious period of the asymptomatic carriers.