This thesis presents the first determination of |Vub| at a hadron collider and in a baryonic decay. The determination is made by measuring the ratio of branching fractions of the baryonic decays $\Lambda^{0}_{b} \rightarrow p \mu^{-} \bar{\nu}_{\mu}$ and $\Lambda^{0}_{b} \rightarrow \Lambda^{+}_{c} \mu^{-} \bar{\nu}_{\mu}$ at large momentum transfer squared. The experimental measurement was made using a $2$ fb$^{-1}$ dataset of $pp$ collision events produced at $\sqrt{s}= 8$ TeV by the Large Hadron Collider and collected by the LHCb experiment in 2012. This is the first observation of the decay $\Lambda^{0}_{b} \rightarrow p \mu^{-} \bar{\nu}_{\mu}$ for which the branching fraction is measured to be $B_{\Lambda^{0}_{b} \rightarrow p \mu^{-} \bar{\nu}_{\mu}} = (4.1 \pm 1.0) \times 10^{-4}$. Combining the measured experimental ratio with the latest Lattice QCD predictions for the form factors of $\Lambda^{0}_{b} \rightarrow p \mu^{-} \bar{\nu}_{\mu}$ and $\Lambda^{0}_{b} \rightarrow \Lambda^{+}_{c} \mu^{-} \bar{\nu}_{\mu}$ decays results in a determination of the ratio of CKM elements, |Vub|/ |Vcb| = 0.083 \pm 0.004 \pm 0.004$, where the first uncertainty is experimental and the second uncertainty is theoretical. This precision determination of |Vub|/| |Vcb| provides an important constraint for global fits of the CKM sector of the Standard Model. Finally, combining the ratio CKM elements, |Vub|/| |Vcb| with the world average of |Vcb| from exclusive measurements allows for a determination of the CKM matrix element |Vub| = (3.27 \pm 0. 15 \pm 0.16 \pm 0.06)\times10^{-3}$. Here the first uncertainty is experimental, the second uncertainty is theoretical and the final uncertainty is from |Vcb| While the measurement agrees well with measurements of |Vub| made using $\bar{B}^{0} \rightarrow \pi^{+} l^{-} \bar{\nu}_{l}$ decays the measurement is $3.5\sigma$ below the world average of |Vub| from inclusive $B \rightarrow X_{u} l^{-} \bar{\nu}_{l}$ decays. This reinforces the long-standing tension between inclusive and exclusive measurements of |Vub|.