Question 23 to 23 are based on this passage
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Few mathematical constructs seem as conceptually simple as that of randomness. According to the traditional definition, a number is random if it is chosen purely as the result of a probabilistic mechanism such as the roll of a fair die. In their groundbreaking work regarding complexity and the limitations of formal systems, mathematicians Gregory Chaitin and A.N. Kolmogorov force us to consider this last claim more closely.

Consider two possible outcomes of throwing a fair die three times: first, 1, 6, and 2; second 3, 3, and 3. Now let us construct two three-member sets based on the results. Though the first set—{1,6,2}—intuitively seems more random than the second—{3,3,3}, they are each as likely to occur, and thus according to the accepted definition, must be considered equally random. This unwelcome result prompts Chaitin and Kolmogorov to suggest the need for a new standard of randomness, one that relies on the internal coherence of the set as opposed to its origin.

Question 23

Consider each of the choices separately and select all that apply.

Which of the following is an inference made in the passage above?

A. The results of the same probabilistic mechanism will each be as likely as the other to occur.

B. According to the traditional definition of randomness, two numbers should be considered equally random if they result from the same probabilistic mechanism.

C. Different probabilistic mechanisms are likely to result in similar outcomes.

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