XAT 2014 — VARC Question 17
Analyze the following passage and provide appropriate answers for the questions that follow.
Ideas involving the theory probability play a decisive part in modern physics. Yet we will still lack a satisfactory, consistence definition of probability; or, what amounts to much the same, we still lack a satisfactory axiomatic system for the calculus of probability. The relations between probability and experience are also still in need of clarification. In investigating this problem we shall discover what will at first seem an almost insuperable objection to my methodological views. For although probability statements play such a vitally important role in empirical science, they turn out to be in principle impervious to strict falsification. Yet this very stumbling block will become a touchstone upon which to test my theory, in order to find out what it is worth. Thus, we are confronted with two tasks. The first is to provide new foundations for the calculus of probability. This I shall try to do by developing the theory of probability as a frequency theory, along the lines followed by Richard von Mises, But without the use of what he calls the ‘axiom of convergence’ (or ‘limit axiom’) and with a somewhat weakened ‘axiom of randomness’ The second task is to elucidate the relations between probability and experience. This means solving what I call the problem of decidability statements. My hope is that the investigations will help to relieve the present unsatisfactory situation in which physicists make much use of probabilities without being able to say, consistently, what they mean by ‘probability’.
The statement, “The relations between probability and experience are still in need of clarification” implies that:
Answer & solution
- A
Probability of an event can always be checked with experience.
- B
Probability of an event can only be gauged historically.
- C
Probability is mathematical while experience is real.
Probability statements can become difficult to disprove without experience.
- E
Probability is futuristic.
The given statement “The relations between probability and experience are still in need of clarification” hints that while probability and experience are linked, their precise relationship requires further elucidation.
Option 1 can be eliminated because of the word “always” which indicates a precise relationship between experience and probability.
Option 2 can be eliminated due to similar reasons, as it indicates that probability is entirely dependent on history.
Option 3 distinguishes probability from experience by calling one “real” and the other “mathematical”; no such comparison has been made in the passage.
Option 5 can be eliminated since the implications of the future on probability are not suggested in the passage.
Option 4 alone holds since it does not dispute the link between “probability” and “experience” and is vindicated from the lines - “The second task is to elucidate the relations between … decidability of probability statements”.
Hence, the correct answer is option 4.