Ideas involving the theory of probability play a decisive part in modern physics. Yet we still lack a satisfactory, consistent 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:
Show Hint
- Probability of an event can always be checked with experience.
- Probability of an event can only be gauged historically.
- Probability is mathematical while experience is real.
- Probability statements can become difficult to disprove without experience.
- Probability is futuristic.
The Correct Option is C
Solution and Explanation
The passage stresses that probability lacks a consistent definition and that its relation to real-world experience remains unclear. Probability operates as a formal/mathematical tool, whereas experience deals with actual events and observations.
Step 2: Examine each option.
(A) “Probability can always be checked with experience” — not true; the passage emphasizes the difficulty of aligning probability with experience.
(B) “Only gauged historically” — too narrow; the passage does not confine probability to history.
(C) “Probability is mathematical while experience is real” — matches the passage, which highlights the gap between abstract probability theory and real empirical outcomes.
(D) “Probability statements difficult to disprove without experience” — partly true, but not the central implication of the author’s statement.
(E) “Probability is futuristic” — irrelevant.
Step 3: Conclusion.
The correct inference is that probability functions as an abstract/mathematical framework, while experience is grounded in reality, and the relation between the two is not yet clarified.
\[ \boxed{\text{Probability is mathematical while experience is real.}} \]
Author has talked about the two tasks in the above passage. Choose the best option from the following statements relevant to the tasks.
Show Hint
- The first task is sufficient to become the touchstone for the author to test his theory.
- The second task is sufficient to become the touchstone for the author to test his theory.
- Either of the tasks is sufficient for the author to test his theory.
- None of the tasks is sufficient for the author to test his theory.
- Both the tasks would be important for the author to test his theory.
The Correct Option is
Solution and Explanation
The author clearly mentions:
1. To provide new foundations for the calculus of probability.
2. To elucidate the relations between probability and experience.
Step 2: Evaluate their role.
The passage explains that the problem of probability cannot be solved by focusing only on mathematics or only on experience. Both the theoretical framework (task 1) and the experiential clarification (task 2) are necessary to test and validate the author’s methodological views.
Step 3: Eliminate wrong options.
(A) and (B) — claim sufficiency of only one task. This contradicts the passage.
(C) — “either is sufficient” is incorrect; the passage stresses both are required.
(D) — “none is sufficient” is also false.
Step 4: Correct option.
(E) — reflects the author’s emphasis that both tasks are equally important and together form the touchstone to test his theory.
\[ \boxed{\text{Both the tasks would be important for the author to test his theory.}} \]
Which one of the following statements can be inferred from the passage?
Show Hint
- Physics is the only subject that borrows from the theory.
- Physics is the only subject where the theory of probability is inaccurately applied.
- The theory of probability may be inaccurately applied in other subjects.
- Physics is highly mathematical.
- Experience relates to physical objects only.
The Correct Option is D
Solution and Explanation
The passage emphasized that probability theory plays a decisive role in modern physics. It also mentioned the lack of a satisfactory axiomatic foundation for probability, showing that probability in physics is deeply tied to mathematical formulations.
Step 2: Evaluate options.
(A) Incorrect — the passage does not claim that only physics borrows from probability; other sciences may too.
(B) Incorrect — it does not restrict inaccuracies only to physics.
(C) Incorrect — while probability may apply elsewhere, the passage does not explicitly suggest inaccuracies in other subjects.
(D) Correct — the passage’s repeated emphasis on mathematical probability being central to physics supports this inference: physics is highly mathematical.
(E) Incorrect — experience is contrasted with probability, but not restricted only to physical objects.
Step 3: Conclusion.
Thus, the best inference is that the passage highlights physics as a subject strongly tied to mathematics through probability theory.
\[ \boxed{\text{Physics is highly mathematical.}} \]
Top Questions on Reading Comprehension
No one argues that the rich should be rich because they were born to wealthy parents. Critics of inequality may complain that those who would abolish inheritance taxes, say, are implicitly endorsing hereditary privilege. But no one defends hereditary privilege outright or disputes the principle that careers should be open to talents.
Most of our debates about access to jobs, education, and public o ce proceed from the premise of equal opportunity. Our disagreements are less about the principle itself than about what it requires. For example, critics of a rmative action in hiring and college admissions argue that such policies are inconsistent with equality of opportunity, because they judge applicants on factors other than merit. Defenders of a rmative action reply that such policies are necessary to make equality of opportunity a reality for members of groups that have suffered discrimination or disadvantage.
At the level of principle at least, and political rhetoric, meritocracy has won the day. In democracies throughout the world, politicians of the center-left and center-right claim that their policies are the ones that will enable all citizens, whatever their race or ethnicity, gender or class, to compete on equal terms and to rise as far as their efforts and talents will take them. When people complain about meritocracy, the complaint is usually not about the ideal but about our failure to live up to it: The wealthy and powerful have rigged the system to perpetuate their privilege; the professional classes have gured out how to pass their advantages on to their children, converting the meritocracy into a hereditary aristocracy; colleges that claim to select students on merit give an edge to the sons and daughters of the wealthy and the well-connected. According to this complaint, meritocracy is a myth, a distant promise yet to be redeemed.- XAT - 2025
- Verbal and Logical Ability
- Reading Comprehension
Look how you turned on
the ceiling fan—it’s too high,
see how it shakes and trembles.
You walk into this room
with your hot ideas
and the ceiling fan has to work harder
to cool down the room
for us. You walk into this room
with your crazy eyes
and the ceiling fan
wants to y loose. It dreams
of becoming a spider lily.- XAT - 2025
- Verbal and Logical Ability
- Reading Comprehension
Recently, a team of social scientists launched an experiment to test that hypothesis. They recruited 1,500 entrepreneurs in West Africa—a mix of women and men in their 30s, 40s, and 50s—who were running small startups in manufacturing, service, and commerce. They randomly assigned the founders to one of three groups. One was a control group: they went about their business as usual. The other two were training groups: they spent a week learning new concepts, analyzing them in case studies of other entrepreneurs, and applying them to their own startups through role-play and re section exercises. What differed was whether the training focused on cognitive skills or character skills. In cognitive skills training, the founders took an accredited business course created by the International Finance Corporation. They studied nance, accounting, HR, marketing, and pricing, and practiced using what they learned to solve challenges and seize opportunities. In character skills training, the founders attended a class designed by psychologists to teach personal initiative. They studied proactivity, discipline, and determination, and practiced putting those qualities into action. Character skills training had a dramatic impact. After founders had spent merely ve days working on these skills, their rms’ pro ts grew by an average of 30 percent over the next two years. That was nearly triple the bene t of training in cognitive skills. Finance and marketing knowledge might have equipped founders to capitalize on opportunities, but studying proactivity and discipline enabled them to generate opportunities. They learned to anticipate market changes rather than react to them. They developed more creative ideas and introduced more new products. When they encountered nancial obstacles, instead of giving up, they were more resilient and resourceful in seeking loans. Along with demonstrating that character skills can propel us to achieve greater things, this evidence reveals that it’s never too late to build them … Character doesn’t set like plaster—it retains its plasticity. Character is often confused with personality, but they’re not the same. Personality is your predisposition—your basic instincts for how to think, feel, and act. Character is your capacity to prioritize your values over your instincts. Knowing your principles doesn’t necessarily mean you know how to practice them, particularly under stress or pressure. It’s easy to be proactive and determined when things are going well. The true test of character is whether you manage to stand by those values when the deck is stacked against you. If personality is how you respond on a typical day, character is how you show up on a hard day. Personality is not your destiny—it’s your tendency. Character skills enable you to transcend that tendency to be true to your principles. It’s not about the traits you have—it’s what you decide to do with them. Wherever you are today, there’s no reason why you can’t grow your character skills starting now.
- XAT - 2025
- Verbal and Logical Ability
- Reading Comprehension
This uidity and situational dependence is uniquely human. In other species, in-group/outgroup distinctions re ect degrees of biological relatedness, or what evolutionary biologists call “kin selection.” Rodents distinguish between a sibling, a cousin, and a stranger by smell—xed, genetically determined pheromonal signatures—and adapt their cooperation accordingly. Those murderous groups of chimps are largely made up of brothers or cousins who grew up together and predominantly harm outsiders. Humans are plenty capable of kin-selective violence themselves, yet human group mentality is often utterly independent of such instinctual familial bonds. Most modern human societies rely instead on cultural kin selection, a process allowing people to feel closely related to what are, in a biological sense, total strangers. Often, this requires a highly active process of inculcation, with its attendant rituals and vocabularies. Consider military drills producing “bands of brothers,” unrelated college freshmen becoming sorority “sisters,” or the bygone value of welcoming immigrants into “the American family.” This malleable, rather than genetically xed, path of identity formation also drives people to adopt arbitrary markers that enable them to spot their cultural kin in an ocean of strangers—hence the importance various communities attach to ags, dress, or facial hair. The hipster beard, the turban, and the “Make America Great Again” hat all fulfill this role by sending strong signals of tribal belonging. Moreover, these cultural communities are arbitrary when compared to the relatively axed logic of biological kin selection. Few things show this arbitrariness better than the experience of immigrant families, where the randomness of a visa lottery can radically reshu e a child’s education, career opportunities, and cultural predilections. Had my grandparents and father missed the train out of Moscow that they instead barely made, maybe I’d be a chain smoking Russian academic rather than a Birkenstock-wearing American one, moved to tears by the heroism during the Battle of Stalingrad rather than that at Pearl Harbor. Scaled up from the level of individual family histories, our big-picture group identities—the national identities and cultural principles that structure our lives— are just as arbitrary and subject to the vagaries of history.
- XAT - 2025
- Verbal and Logical Ability
- Reading Comprehension
- Work, for many on the career track, is greedy. The individual who puts in overtime, weekend time, or evening time will earn a lot more—so much more that, even on an hourly basis, the person is earning more.…The greediness of work means that couples with children or other care responsibilities would gain by doing a bit of specialization. This specialization doesn’t mean catapulting back to the world of Leave It to Beaver. Women will still pursue demanding careers. But one member of the couple will be on call at home, ready to leave the o ce or workplace at a moment’s notice. That person will have a position with considerable exibility and will ordinarily not be expected to answer an e-mail or a call at ten p.m. That parent will not have to cancel an appearance at soccer practice for an M \& A. The other parent, however, will be on call at work and do just the opposite. The potential impact on promotion, advancement, and earnings is obvious. The work of professionals and managers has always been greedy. Lawyers have always burned the midnight oil. Academics have always been judged for their cerebral output and are expected not to turn their brains off in the evenings. Most doctors and veterinarians were once on call 24/7. The value of greedy jobs has greatly increased with rising income inequality, which has soared since the early 1980s. Earnings at the very upper end of the income distribution have ballooned. The worker who jumps the highest gets an ever-bigger reward. The jobs with the greatest demands for long hours and the least exibility have paid disproportionately more, while earnings in other employments have stagnated. Thus, positions that have been more di cult for women to enter in the rst place, such as those in nance, are precisely the ones that have seen the greatest increases in income in the last several decades. The private equity associate who sees the deal through from beginning to end, who did the di cult modeling, and who went to every meeting and late-night dinner, will have maximum chance for a big bonus and the sought-after promotion. Rising inequality in earnings may be one important reason why the gender pay gap among college graduates has remained at in the last several decades, despite improvements in women’s credentials and positions. It may be the reason why the gender earnings gap for college graduates became larger than that between men and women in the entire population in the late 1980s and early 1990s. Women have been swimming upstream, holding their own but going against a strong current of endemic income inequality. Greedy work also means that couple equity has been, and will continue to be, jettisoned for increased family income. And when couple equity is thrown out the window, gender equality generally goes with it, except among same-sex unions. Gender norms that we have inherited get reinforced in a host of ways to allot more of the childcare responsibility to mothers, and more of the family care to grown daughters. 68. Which of the following statements CANNOT be inferred from the passage?
- XAT - 2025
- Verbal and Logical Ability
- Reading Comprehension
Questions Asked in XAT exam
Match the following renowned Indian personalities with their respective awards.
Names Award 1. Shri Ratan Naval Tata A. Dadasaheb Phalke Award 2. Manmohan Singh B. Grammy Awards 3. Zakir Hussain C. Carnegie Medal of Philanthropy 4. Shyam Benegal D. World Statesman Award - XAT - 2025
- Famous personalities and their contributions
Match the following authors with their respective works.
Authors Books 1. Andy Weir A. Dune 2. Cixin Liu B. The Time Machine 3. Stephen Hawking C. The Brief History of Time 4. HG Wells D. The Martian 5. Frank Herbert E. The Three Body Problem - XAT - 2025
- Books and Authors
Match the following airlines with the countries where they are headquartered.
Airlines Countries 1. AirAsia A. Singapore 2. AZAL B. South Korea 3. Jeju Air C. Azerbaijan 4. Indigo D. India 5. Tigerair E. Malaysia - XAT - 2025
- Business and Economy
The diagram below represents a road network connecting five towns, namely Meeren, Lannisport, Winterfell, Oldtown, and Gulltown. The maximum speed limits along any stretch of road are as shown in the diagram. The straight road that connects Meeren to Gulltown passes through Oldtown. Another straight road, running west to east, connecting Meeren to Winterfell, passes through Lannisport. Further, two straight roads, one from Lannisport to Oldtown and another from Winterfell to Gulltown, are perpendicular to the road joining Meeren to Winterfell, and run from south to north.
Consider a car always travelling at the maximum permissible speed, and always taking the shortest route. It takes 1 hour to reach Oldtown from Meeren, 2 hours to reach Gulltown from Oldtown, and 45 minutes to reach Winterfell from Gulltown. (For this problem, always consider the shortest route in terms of distance.)
- XAT - 2025
- Logical and Analytical Reasoning Skills
The plots below depict and compare the average monthly incomes (in Rs. ’000) of males and females in ten cities of India in the years 2005 and 2015. The ten cities, marked A-J in the records, are of different population sizes. For a fair comparison, to adjust for inflation, incomes for both the periods are scaled to 2025 prices. Each red dot represents the average monthly income of females in a particular city in a particular year, while each blue dot represents the average monthly income of males in a particular city in a particular year. The gender gap for a city, for a particular year, is defined as the absolute value of the average monthly income of males, minus the average monthly income of females, in that year.
- XAT - 2025
- Data Interpretation