Inclusive branching ratios involving b →τ transitions are measured in approximately four million hadronic Z decays collected by the ALEPH detector at LEP. The fully-inclusive branching ratio BR(b →τ−ν¯τ X) and the semi-inclusive branching ratio BR(b →τ−ν¯τD∗± X) are measured to be (2.43±0.20±0.25) and (0.88±0.31±0.28) , in agreement with the standard model predictions. Upper limits on the branching fractions BR(B −→τ−ν¯τ) and BR(b →sνν¯) are set to 8.3×10−4 and 6.4×10−4 at the 90% C.L. These results allow a 90% C.L. lower limit of 0.40 GeV/ c2)−1 to be set on the tanβ/mH± ratio, in the framework of type-II two-Higgs-doublet models.