 Setting the probability p_e = 1 for all e \in E, the stochastic problem becomes the classical online bipartite matching problem . Our competitive ratios thus generalize corresponding results for the classical ROM bipartite matching setting .
<clarity>  Setting the probability p_e = 1 for all e \in E, the stochastic problem becomes the classical online bipartite matching problem . Our competitive ratios thus generalize corresponding results for the classical ROM bipartite matching setting .
 Setting the probability p_e = 1 for all e \in E, the stochastic problem becomes the classical online bipartite matching problem , and so our main contribution is in making progress towards understanding which classical results extend to the stochastic probing model .