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Generating a random vector with elements in specified range

I would like to generate a random vector in which its elements are between 0 and 1 (including 0 and 1). As far as I know, v = random_matrix(ZZ, 1, 10) is a way to generate a random matrix. How would I restrict the elements to the range I want?

I am trying to build a function with a probability input, and then compare the probability to each of the elements separately in the random vector.