Given that: \[ x + \frac{100}{x} > 29 \Rightarrow x^2 - 29x + 100 > 0 \] This simplifies to: \[ (x - 4)(x - 25) > 0 \] Solving this inequality: \[ x > 25 \quad \text{or} \quad x < 4 \] Thus, \( x \) can take a total of 78 values (1, 2, 3, 26, ..., 100). The required probability is: \[ \frac{78}{100} = \frac{39}{50} \]