We have measured the number of like-sign (LS) and opposite-sign (OS) lepton pairs arising from double semileptonic decays of b and b¯ hadrons, pair produced at the Fermilab Tevatron collider. The data samples were collected with the Collider Detector at Fermilab during the 1992–1995 collider run by triggering on the existence of μμ or eμ candidates in an event. The observed ratio of LS to OS dileptons leads to a measurement of the average time-integrated mixing probability of all produced b-flavored hadrons which decay weakly, χ¯=0.152±0.007(stat)±0.011(syst), that is significantly larger than the world average χ¯=0.118±0.005.