A hydrophilic fluid containing a hydrophobic component at low concentration, which is confined between hydrophobic surfaces, has been revisited using the RISM-HNC theory with a simple model. When strength of the attractive interaction between the hydrophilic molecules is considerably high, as in the case of water, the presence of even a trace amount of hydrophobic molecules affects the behavior of the confined fluid to a drastic extent. The phase transition, appearance of the second phase of the hydrophobic molecules in the confined domain, and the long-range surface forces are analyzed and discussed in detail.