This paper investigates probabilistic versions of degenerate Fubini polynomials and their order-$r$ analogues, focusing on the probabilistic degenerate Fubini polynomials associated with a random variable \( Y \). The authors derive explicit expressions, identities, and recurrence relations for these polynomials. They consider specific cases where \( Y \) is a gamma random variable, a Poisson random variable, and a Bernoulli random variable. Key results include: 1. **Explicit Expressions**: The probabilistic degenerate Fubini polynomials \( F_{n,\lambda}^Y(x) \) are expressed in terms of sums involving the moment generating function of \( Y \) and the probabilistic degenerate Stirling numbers of the second kind. 2. **Recurrence Relations**: Recurrence relations for \( F_{n,\lambda}^Y(x) \) are derived, providing a way to compute the polynomials for higher values of \( n \). 3. **Derivatives and Identities**: The \( r \)-th derivative of \( F_{n,\lambda}^Y(x) \) is expressed in terms of other probabilistic degenerate Fubini polynomials, and identities involving these polynomials are established. 4. **Special Cases**: Specific expressions for \( F_{n,\lambda}^Y(x) \) are given when \( Y \) follows a gamma distribution, a Poisson distribution, and a Bernoulli distribution. The paper concludes with future research directions, including further exploration of degenerate versions, \(\lambda\)-analogues, and probabilistic versions of special polynomials and numbers, and their potential applications in various fields.This paper investigates probabilistic versions of degenerate Fubini polynomials and their order-$r$ analogues, focusing on the probabilistic degenerate Fubini polynomials associated with a random variable \( Y \). The authors derive explicit expressions, identities, and recurrence relations for these polynomials. They consider specific cases where \( Y \) is a gamma random variable, a Poisson random variable, and a Bernoulli random variable. Key results include: 1. **Explicit Expressions**: The probabilistic degenerate Fubini polynomials \( F_{n,\lambda}^Y(x) \) are expressed in terms of sums involving the moment generating function of \( Y \) and the probabilistic degenerate Stirling numbers of the second kind. 2. **Recurrence Relations**: Recurrence relations for \( F_{n,\lambda}^Y(x) \) are derived, providing a way to compute the polynomials for higher values of \( n \). 3. **Derivatives and Identities**: The \( r \)-th derivative of \( F_{n,\lambda}^Y(x) \) is expressed in terms of other probabilistic degenerate Fubini polynomials, and identities involving these polynomials are established. 4. **Special Cases**: Specific expressions for \( F_{n,\lambda}^Y(x) \) are given when \( Y \) follows a gamma distribution, a Poisson distribution, and a Bernoulli distribution. The paper concludes with future research directions, including further exploration of degenerate versions, \(\lambda\)-analogues, and probabilistic versions of special polynomials and numbers, and their potential applications in various fields.