The Idea of Probability
... will contain a collectible card featuring one of these NASCAR drivers: Jeff Gordon, Dale Earnhardt, Jr., Tony Stewart, Danica Patrick, or Jimmie Johnson. The company says that each of the 5 cards is equally likely to appear in any box of cereal. A NASCAR fan decides to keep buying boxes of the cerea ...
... will contain a collectible card featuring one of these NASCAR drivers: Jeff Gordon, Dale Earnhardt, Jr., Tony Stewart, Danica Patrick, or Jimmie Johnson. The company says that each of the 5 cards is equally likely to appear in any box of cereal. A NASCAR fan decides to keep buying boxes of the cerea ...
L70
... the bag. Then, a second marble is drawn and dropped back in the bag. Both marbles were red. If another marble is drawn, what is the probability that it will be red? ...
... the bag. Then, a second marble is drawn and dropped back in the bag. Both marbles were red. If another marble is drawn, what is the probability that it will be red? ...
Probability: History
... Rules much like modern-day craps. Cards introduced 14th Primero: early form of poker. Backgammon etc were also popular during this period. The first instance of anyone conceptualizing probability in terms of a mathematical model occurred in the sixteenth century ...
... Rules much like modern-day craps. Cards introduced 14th Primero: early form of poker. Backgammon etc were also popular during this period. The first instance of anyone conceptualizing probability in terms of a mathematical model occurred in the sixteenth century ...
Lecture5_SP17_probability_history_solutions
... Rules much like modern-day craps. Cards introduced 14th Primero: early form of poker. Backgammon etc were also popular during this period. The first instance of anyone conceptualizing probability in terms of a mathematical model occurred in the sixteenth century ...
... Rules much like modern-day craps. Cards introduced 14th Primero: early form of poker. Backgammon etc were also popular during this period. The first instance of anyone conceptualizing probability in terms of a mathematical model occurred in the sixteenth century ...
Name 8-1 Notes IB Math SL Lesson 8
... Graphical form Table form In functional form as a probability mass function. ...
... Graphical form Table form In functional form as a probability mass function. ...
Probability Theory
... In 1692, John Arbuthnot's translation of Huygens' De Ratiociniis in Ludo Aleae becomes the first publication on probability in the English language. It is titled Of the Laws of Chance, or, a method of Calculation of the Hazards of Game, Plainly demonstrated, And applied to Games as present most in U ...
... In 1692, John Arbuthnot's translation of Huygens' De Ratiociniis in Ludo Aleae becomes the first publication on probability in the English language. It is titled Of the Laws of Chance, or, a method of Calculation of the Hazards of Game, Plainly demonstrated, And applied to Games as present most in U ...
texture
... • Similar structures repeated over and over again • Often has some degree of randomness ...
... • Similar structures repeated over and over again • Often has some degree of randomness ...
Towards Unique Physically Meaningful Definitions of Random and
... Towards a more physically adequate notion of randomness. KolmogorovMartin-Löf definition prevents sequences 00. . . from being called random. This prevention makes perfect physical sense: if we flip a coin and every time get tail, this clearly is not a fair coin. However, one can easily check that f ...
... Towards a more physically adequate notion of randomness. KolmogorovMartin-Löf definition prevents sequences 00. . . from being called random. This prevention makes perfect physical sense: if we flip a coin and every time get tail, this clearly is not a fair coin. However, one can easily check that f ...
Probability Density Functions A continuous random variable takes
... A continuous random variable takes on an uncountably infinite number of possible values. For a discrete random variable X that takes on a finite or countably infinite number of possible values, we determined P(X = x) for all of the possible values of X, and called it the probability mass function (" ...
... A continuous random variable takes on an uncountably infinite number of possible values. For a discrete random variable X that takes on a finite or countably infinite number of possible values, we determined P(X = x) for all of the possible values of X, and called it the probability mass function (" ...
COMP245: Probability and Statistics 2016
... (b) If a pack is chosen at random and two components from it are tested, what is the probability that exactly one of the components tested is satisfactory? (c) If it was found that just one of the components tested was satisfactory, what is the probability that the selected pack contained medium qua ...
... (b) If a pack is chosen at random and two components from it are tested, what is the probability that exactly one of the components tested is satisfactory? (c) If it was found that just one of the components tested was satisfactory, what is the probability that the selected pack contained medium qua ...
p - Tanya Khovanova
... The probability that an ordered pair of kids is mixed is (8x7 +7*8)/15x14 = 8/15; thus each of the 14 adjacent pairs of seats has 8/15 mixed pairs in it on average. Since expectations add regardless of dependence, the expected number of mixed adjacent pairs is 14x8/15 = 212/15. 100 passengers on a t ...
... The probability that an ordered pair of kids is mixed is (8x7 +7*8)/15x14 = 8/15; thus each of the 14 adjacent pairs of seats has 8/15 mixed pairs in it on average. Since expectations add regardless of dependence, the expected number of mixed adjacent pairs is 14x8/15 = 212/15. 100 passengers on a t ...
Economics 302 Quiz #1
... of the United States, there are 434 municipal governments in the state. (12 points) a. How would you choose a systematic sample of 10 municipalities? ...
... of the United States, there are 434 municipal governments in the state. (12 points) a. How would you choose a systematic sample of 10 municipalities? ...
TOWARDS UNIQUE PHYSICALLY MEANINGFUL DEFINITIONS OF
... Towards a more physically adequate notion of randomness. KolmogorovMartin-Löf definition prevents sequences 00. . . from being called random. This prevention makes perfect physical sense: if we flip a coin and every time get tail, this clearly is not a fair coin. However, one can easily check that f ...
... Towards a more physically adequate notion of randomness. KolmogorovMartin-Löf definition prevents sequences 00. . . from being called random. This prevention makes perfect physical sense: if we flip a coin and every time get tail, this clearly is not a fair coin. However, one can easily check that f ...
COMP 245 Statistics Exercises 2
... 2. Suppose two events E and F are mutually exclusive. State the precise conditions under which they may also be independent. 3. What is the probability that a single roll of a die will give an odd number if (a) no other information is given; (b) you are told that the number is less than 4. ...
... 2. Suppose two events E and F are mutually exclusive. State the precise conditions under which they may also be independent. 3. What is the probability that a single roll of a die will give an odd number if (a) no other information is given; (b) you are told that the number is less than 4. ...
using experimental approaches for teaching probability
... School of public schools in the State of São Paulo, Brazil. Those teachers have already been participating in that group, working with other themes of their classroom practice. They proposed to work with Probability, alleging to have difficulties for preparing instruction because of the gaps in thei ...
... School of public schools in the State of São Paulo, Brazil. Those teachers have already been participating in that group, working with other themes of their classroom practice. They proposed to work with Probability, alleging to have difficulties for preparing instruction because of the gaps in thei ...
Infinite Monkey Theorem
... buying 4 lottery tickets consecutively and winning the jackpot each time. In the case of the entire text of Hamlet, the probabilities are so vanishingly small they can barely be conceived in human terms. The text of Hamlet, even stripped of all punctuation, contains well over 130,000 letters which w ...
... buying 4 lottery tickets consecutively and winning the jackpot each time. In the case of the entire text of Hamlet, the probabilities are so vanishingly small they can barely be conceived in human terms. The text of Hamlet, even stripped of all punctuation, contains well over 130,000 letters which w ...
Full text in PDF form
... long-standing lack of a solid basis for the understanding of randomness. Measure theory provided a sound axiomatic foundation for probability theory from the pure mathematics standpoint, but begged the question of the applicability of the axioms. Although the issue has by no means been completely re ...
... long-standing lack of a solid basis for the understanding of randomness. Measure theory provided a sound axiomatic foundation for probability theory from the pure mathematics standpoint, but begged the question of the applicability of the axioms. Although the issue has by no means been completely re ...
PDF
... Description. The aim of this course is to provide an introduction to nonasymptotic methods for the study of random structures in high dimension that arise in probability, statistics, computer science, and mathematics. The emphasis is on the development of a common set of tools that has proved to be ...
... Description. The aim of this course is to provide an introduction to nonasymptotic methods for the study of random structures in high dimension that arise in probability, statistics, computer science, and mathematics. The emphasis is on the development of a common set of tools that has proved to be ...
Ch. 4-6 PowerPoint Review
... P(A or B) = P(A) + P(B) - P(A and B) P(A and B) = P(A) P(B|A) A and B are independent if and only if P(B) = P(B|A) ...
... P(A or B) = P(A) + P(B) - P(A and B) P(A and B) = P(A) P(B|A) A and B are independent if and only if P(B) = P(B|A) ...
training teachers to teach probability
... concepts, and even there still different views about the nature of probability (Fine, 1971). Borovcnik and Peard (1996) remark that counterintuitive results in probability are found even at very elementary levels, whereas in other branches of mathematics counterintuitive results are encountered only ...
... concepts, and even there still different views about the nature of probability (Fine, 1971). Borovcnik and Peard (1996) remark that counterintuitive results in probability are found even at very elementary levels, whereas in other branches of mathematics counterintuitive results are encountered only ...
Student Worksheet From Probability to the Gambler`s Fallacy
... become the most important object of human knowledge … The most important questions of life are, for the most part, really only problems of probability.” ~ Pierre Simon, Marquis de LaPlace, Theorie Analytique des Probabilites, 1812. Gambling is a human activity that can involve probability calculatio ...
... become the most important object of human knowledge … The most important questions of life are, for the most part, really only problems of probability.” ~ Pierre Simon, Marquis de LaPlace, Theorie Analytique des Probabilites, 1812. Gambling is a human activity that can involve probability calculatio ...
Section 5.1 Introduction to Probability and
... if I toss the coin 10 times, I should get 5 Heads. However, with such a small number of tosses there is a lot of room for variability. There ...
... if I toss the coin 10 times, I should get 5 Heads. However, with such a small number of tosses there is a lot of room for variability. There ...
Certain, impossible, event, mutually exclusive, conditional, bias
... 1) What is the probability of picking a vowel from the letters MRS MARSHALL? 2) Which is more likely- rolling a prime number on an ordinary 6 sided dice, or rolling a square number? 3) What is the probability of picking an S out of the letters MISSISSIPPI? 4) The probability I pass a test is 0.8, wh ...
... 1) What is the probability of picking a vowel from the letters MRS MARSHALL? 2) Which is more likely- rolling a prime number on an ordinary 6 sided dice, or rolling a square number? 3) What is the probability of picking an S out of the letters MISSISSIPPI? 4) The probability I pass a test is 0.8, wh ...
The meaning of randomness for secondary school
... With the first theoretical developments of probability, randomness was related to equi-probability (for example in the Liber of Ludo Aleae by Cardano), because this development was closely linked to games of chance, where the number of possibilities is finite and the principle of equal probabilities ...
... With the first theoretical developments of probability, randomness was related to equi-probability (for example in the Liber of Ludo Aleae by Cardano), because this development was closely linked to games of chance, where the number of possibilities is finite and the principle of equal probabilities ...
History of randomness
In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. At the same time, most ancient cultures used various methods of divination to attempt to circumvent randomness and fate.The Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the sixteenth century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of modern calculus had a positive impact on the formal study of randomness. In the 19th century the concept of entropy was introduced in physics.The early part of the twentieth century saw a rapid growth in the formal analysis of randomness, and mathematical foundations for probability were introduced, leading to its axiomatization in 1933. At the same time, the advent of quantum mechanics changed the scientific perspective on determinacy. In the mid to late 20th-century, ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness.Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the twentieth century computer scientists began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases, such randomized algorithms are able to outperform the best deterministic methods.