The ALICE experiment at the LHC has studied J/ψ production at midrapidity in pp collisions at √s = 7TeV through its electron pair decay on a data sample corresponding to an integrated luminosity Lint = 5.6 nb-1. The fraction of J/ψ from the decay of long-lived beauty hadrons was determined for J/ψ candidates with transverse momentum pt > 1.3GeV/c and rapidity |y| < 0.9. The cross section for prompt J/ψ mesons, i.e. directly produced J/ψ and prompt decays of heavier charmonium states such as the ψ(2S) and c resonances, is σprompt J/ψ (pt > 1.3 GeV/c, |y| < 0.9) = 8.3+0.8 (stat.)±} 1.1 (syst.) +1.5 -1.4 (syst. pol.) μb. The cross section for the production of b-hadrons decaying to J/ψ with pt > 1.3GeV/c and |y| < 0.9 is σJ/ψ←hB (pt > 1.3 GeV/c, |y| < 0.9) = 1.46±} 0.38 (stat.) +0.26 -0.32 (syst.) μb. The results are compared to QCD model predictions. The shape of the pt and y distributions of b-quarks predicted by perturbative QCD model calculations are used to extrapolate the measured cross section to derive the bb pair total cross section and dσ/dy at mid-rapidity. © SISSA 2012.