We consider the problem of a retailer that is served by multiple suppliers, where any given supplier, who leads to random yield in orders, is defined to be unreliable. We examine how random yield affects the outcome of supplier selection and the retailer's profit in two cases: independent random yields (IRY) and correlated random yields (CRY). For the IRY, we show that the wholesale price generally takes precedence over reliability in the retailer's supplier selection, that is, a given supplier will be selected only if all less-expensive suppliers are selected, regardless of the given supplier's reliability level. For the CRY, we show that the results may be totally different from results obtained in the IRY. That is, a given supplier is selected but not all less-expensive suppliers are selected. Moreover, we examine the impacts of yield uncertainty on the retailer's profit. We show that the retailer might be better off under unreliable suppliers than under completely reliable suppliers.