1.
What can be used to reverse conditional probability?
Correct Answer
A. Baye's theorem
Explanation
Bayes' theorem is a mathematical formula that can be used to reverse conditional probability. It allows us to calculate the probability of an event A given that event B has already occurred, by using the probability of event B given event A and the individual probabilities of event A and event B. This theorem is widely used in various fields, including statistics, machine learning, and data analysis, to update probabilities based on new evidence or information. Therefore, Bayes' theorem is the correct answer for reversing conditional probability.
2.
The conditional probability of A given B is defined as the quotient of the probability of the joint of events A and B, and the probability of B. Whose definition is this?
Correct Answer
C. Kolmogrov
Explanation
The definition of conditional probability given in the question is attributed to Kolmogorov.
3.
Which of these authors prefers to introduce conditional probability as an axiom of probability?
Correct Answer
B. De finetti
Explanation
De Finetti is the author who prefers to introduce conditional probability as an axiom of probability. This means that he believes that conditional probability should be a fundamental principle or assumption in probability theory. This approach is different from other authors who may introduce conditional probability as a derived concept or define it in terms of other probability concepts.
4.
What is a specified subset of an outcome called?
Correct Answer
B. Event
Explanation
A specified subset of an outcome is called an event.
5.
Which of these describes the behavior of an event?
Correct Answer
C. Law of large numbers
Explanation
The behavior of an event is described by the Law of large numbers. This law states that as the number of trials or observations of an event increases, the average outcome of those trials will converge to the expected value. In other words, the more times an event is repeated, the closer the observed results will be to the predicted probability. This law is commonly used in statistics and probability theory to understand the long-term behavior of random events.
6.
Probability is essential to what type of data analysis?
Correct Answer
D. Quantitative
Explanation
Probability is essential to quantitative data analysis because it provides a way to measure and predict the likelihood of different outcomes or events in numerical terms. Quantitative data involves numerical values and can be analyzed using statistical methods, which often rely on probability theory. By calculating probabilities, researchers can make informed decisions, draw conclusions, and make predictions based on the data.
7.
Which of these is not a central subject of probability?
Correct Answer
B. Space and Event
Explanation
The central subjects of probability include stochastic processes, probability distributions, and discrete random variables. However, space and event are not considered central subjects of probability. Probability theory primarily focuses on the study of uncertainty and the likelihood of events occurring, rather than on the concepts of space and event.
8.
Which of these was a discovery in the twentieth century in Physics?
Correct Answer
D. Probabilistic nature of physical phenomena
Explanation
In the twentieth century, one of the major discoveries in physics was the realization that physical phenomena have a probabilistic nature. This means that instead of being completely deterministic, events in the physical world have an inherent element of randomness. This discovery, often associated with quantum mechanics, challenged the classical view of a clockwork universe and opened up new avenues of understanding in the field of physics.
9.
Who published a book on Probability in 1657 during the early days of probability discovery?
Correct Answer
C. Christiaan Huygens
Explanation
Christiaan Huygens published a book on Probability in 1657 during the early days of probability discovery. Huygens was a Dutch mathematician, astronomer, and physicist who made significant contributions to various fields of science. His book, "De Ratiociniis in Ludo Aleae" (On Reasoning in Games of Chance), laid the foundation for the mathematical theory of probability and introduced concepts such as expected value and the concept of mathematical expectation. Huygens' work played a crucial role in the development of probability theory and its applications in various disciplines.
10.
Who completed the research on mordern day "classic interpretation"?
Correct Answer
A. Pierre Laplace
Explanation
Pierre Laplace completed the research on modern day "classic interpretation".