Consider the following statements:
P: Combinatorics is always invoked in the modeling of physical phenomena.
Q: Modeling some physical phenomena involves assigning probabilities to combinatorial possibilities in order to compute average values of physical quantities.
Based on the passage above, what can be inferred about statements P and Q?
Correct : b
This is a reading comprehension and inference question based strictly on what the passage states.
Statement P — False
P claims combinatorics is "always" used in modeling physical phenomena. The passage uses the word "sometimes" — "This kind of counting is sometimes used in the modeling of several physical phenomena." The word sometimes explicitly means not always. Since the passage only supports a partial/occasional use, the absolute claim in P is not supported. P is false.
Statement Q — True
Q claims that modeling some physical phenomena involves assigning probabilities to combinatorial possibilities to compute average values. The passage states "Often, in such models, the different combinatorial possibilities are assigned probability values. Assigning probabilities enables the computation of the average values of physical quantities." This directly and fully supports Q. Q is true.
Correct answer: B — P is False and Q is True ✓
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