The title of the article is identical to the title of Chapter 21 in Gardner (2001): because we are going to analyze the probability calculations and the ambiguity of the problem statements. We will analyze 3 out of 4 problems from Gardner (2001): broken stick, two boys, three prisoners; and the obtuse random triangle in Hamming (1991) problems. Keywords: Broken stick problem, Obtuse triangle problem, Bertrand's problem, Two sons problem, Three prisoners problem, Monty Hall problem; probability function, probability density, randomness, ambiguity