Final answer:
The probability P(0 < x < 12) for a uniform distribution over the interval [0, 12] with a continuous probability function f(x) = 12 is equal to 1.
Step-by-step explanation:
The question deals with finding the probability of a continuous random variable being within a certain range using a probability function. Considering f(x) is a constant probability function over the interval [0, 12], and its value is given as 12, which indicates a uniform distribution over that interval. The probability P(0 < x < 12) in such a case is simply the area under the probability distribution function between x = 0 and x = 12. Since P(0 ≤ x ≤ 12) = 1 for a probability distribution, and because the distribution is uniform, P(0 < x < 12) would also be equal to 1, since x is bound to fall within the open interval.