This paper introduces and studies probabilistic extensions of degenerate Bernoulli and Euler polynomials. The authors define probabilistic degenerate Bernoulli polynomials associated with a random variable Y and probabilistic degenerate Euler polynomials associated with Y. They also introduce probabilistic degenerate r-Stirling numbers of the second kind and probabilistic degenerate two variable Fubini polynomials associated with Y. The paper derives properties, explicit expressions, recurrence relations, and identities for these polynomials and numbers. As special cases of Y, the authors consider the gamma random variable with parameters α, β > 0, the Poisson random variable with parameter α > 0, and the Bernoulli random variable with probability of success p. The paper also discusses degenerate exponentials, degenerate Bernoulli and Euler polynomials, degenerate Stirling numbers, and degenerate Fubini polynomials. The authors provide explicit expressions for these polynomials and numbers in various cases, including when Y is a gamma, Poisson, or Bernoulli random variable. The paper concludes with a discussion of the properties and applications of these probabilistic degenerate polynomials and numbers.This paper introduces and studies probabilistic extensions of degenerate Bernoulli and Euler polynomials. The authors define probabilistic degenerate Bernoulli polynomials associated with a random variable Y and probabilistic degenerate Euler polynomials associated with Y. They also introduce probabilistic degenerate r-Stirling numbers of the second kind and probabilistic degenerate two variable Fubini polynomials associated with Y. The paper derives properties, explicit expressions, recurrence relations, and identities for these polynomials and numbers. As special cases of Y, the authors consider the gamma random variable with parameters α, β > 0, the Poisson random variable with parameter α > 0, and the Bernoulli random variable with probability of success p. The paper also discusses degenerate exponentials, degenerate Bernoulli and Euler polynomials, degenerate Stirling numbers, and degenerate Fubini polynomials. The authors provide explicit expressions for these polynomials and numbers in various cases, including when Y is a gamma, Poisson, or Bernoulli random variable. The paper concludes with a discussion of the properties and applications of these probabilistic degenerate polynomials and numbers.