We use a rigorous method, based on Bayesian inference, for calculating the odds favoring the hypothesis that any particular class of astronomical transients produce gamma-ray bursts over the hypothesis that they do not. We then apply this method to a sample of 83 Type Ia supernovae and a sample of 20 Type Ib-Ic supernovae. We find overwhelming odds against the hypothesis that all Type Ia supernovae produce gamma-ray bursts, whether at low redshift (109:1) or high-redshift (1012:1), and very large odds (6000:1) against the hypothesis that all Type Ib, Ib/c, and Ic supernovae produce observable gamma-ray bursts. We find large odds (34:1) against the hypothesis that a fraction of Type Ia supernovae produce observable gamma-ray bursts, and moderate odds (6:1) against the hypothesis that a fraction of Type Ib-Ic supernovae produce observable bursts.
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A 1999 study studied this question.