The T-cell (TCR) repertoire relies on the diversity of receptors composed of two chains, called xcexb1 and xcexb2, to recognize pathogens. Using results of high throughput sequencing and computational chain-pairing experiments of human TCR repertoires, we quantitively characterize the xcexb1xcexb2 generation process. We estimate the probabilities of a rescue recombination of the xcexb2 chain on the second chromosome upon failure or success on the first chromosome. Unlike xcexb2 chains, xcexb1 chains recombine simultaneously on both chromosomes, resulting in correlated statistics of the two genes which we predict using a mechanistic model. We find that xe2x88xbc35% of cells express both xcexb1 chains. Altogether, our statistical analysis gives a complete quantitative mechanistic picture that results in the observed correlations in the generative process. We learn that the probability to generate any TCRxcexb1xcexb2 is lower than 10(-12) and estimate the generation diversity and sharing properties of the xcexb1xcexb2 TCR repertoire.