David Hume famously argued that we have no rational basis for believing a claim unless it is logically or mathematically demonstrable. If true, Hume's conclusion would mean that most of our scientific theories are unjustified, as well as many of our more mundane beliefs about the future and the past. Hume's argument -- now called the problem of induction -- remains a central puzzle in epistemology and philosophy of science. Probability theory and statistics are now the primary tools used to quantify certainty and degrees of justification. So we will focus on how these tools might be used to address Hume’s argument. In particular, we will investigate theories of scientific objectivity, interpretations of probability (subjective and objective), and foundational approaches to statistics (frequentist and Bayesian) to assess whether the tools of modern science provide a satisfactory solution to the problem of induction.