Compound Events 15.4
... 26. PASSWORD You forget the last two digits of your password for a website. a. What is the probability that you randomly choose the correct digits? b. Suppose you remember that both digits are even. How does this change the probability that your choices are correct? 27. COMBINATION LOCK The combina ...
... 26. PASSWORD You forget the last two digits of your password for a website. a. What is the probability that you randomly choose the correct digits? b. Suppose you remember that both digits are even. How does this change the probability that your choices are correct? 27. COMBINATION LOCK The combina ...
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... Two events are mutually exclusive, or disjoint events, if they cannot both occur in the same trial of an experiment. For example, rolling a 5 and an even number on a number cube are mutually exclusive events because they cannot both happen at the same time. ...
... Two events are mutually exclusive, or disjoint events, if they cannot both occur in the same trial of an experiment. For example, rolling a 5 and an even number on a number cube are mutually exclusive events because they cannot both happen at the same time. ...
Basic Concepts and Approaches
... Probability-Basic Questions (1) First, there is a question of what we mean when we say that a probability is 0.82, or 0.25. - What is probability? (2) Then, there is the question of how to obtain numerical values of probabilities, i.e., how do we determine that a certain probability is 0.82, or 0.2 ...
... Probability-Basic Questions (1) First, there is a question of what we mean when we say that a probability is 0.82, or 0.25. - What is probability? (2) Then, there is the question of how to obtain numerical values of probabilities, i.e., how do we determine that a certain probability is 0.82, or 0.2 ...
TOPIC 10: BASIC PROBABILITY AND THE HOT HAND 1. The Hot
... Almost everybody has used some conscious or subconscious estimate of the likelihood of an event happening at some point in their life. Such estimates are often based on the relative frequency of the occurrence of the event in similar circumstances in the past and some are based on logical deduction. ...
... Almost everybody has used some conscious or subconscious estimate of the likelihood of an event happening at some point in their life. Such estimates are often based on the relative frequency of the occurrence of the event in similar circumstances in the past and some are based on logical deduction. ...
Processes on complex networks. Percolation
... Two situating are useful to have in mind while discussing what exactly we model by this site percolation. First, you can think of the Internet graph, where vertices are the routers, which are working with probability ϕ and are out of order with probability 1 − ϕ. We are interested in the proportion ...
... Two situating are useful to have in mind while discussing what exactly we model by this site percolation. First, you can think of the Internet graph, where vertices are the routers, which are working with probability ϕ and are out of order with probability 1 − ϕ. We are interested in the proportion ...
Full text PDF - IEJME-Mathematics Education
... students in investigations based on probability experiments, they almost exclusively chose small samples sizes and rarely pooled class data or used representations supportive of examining distributions and variability across collections of samples; so they failed to address the heart of the issue. T ...
... students in investigations based on probability experiments, they almost exclusively chose small samples sizes and rarely pooled class data or used representations supportive of examining distributions and variability across collections of samples; so they failed to address the heart of the issue. T ...
Chapter 4
... Evangelista Torricelli. Pascal also wrote in defense of the scientific method. • Pascal was a mathematician of the first order. He helped create two major new areas of research. He wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with P ...
... Evangelista Torricelli. Pascal also wrote in defense of the scientific method. • Pascal was a mathematician of the first order. He helped create two major new areas of research. He wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with P ...
Ernst Zermelo`s Recurrence Objection
... likely to have a positive or equal negative value; it is then proved that if one combines all possible values of the elementary errors in all possible ways, the great majority of combinations will obey the Gaussian law of errors, and for relatively few combinations will there be significant deviatio ...
... likely to have a positive or equal negative value; it is then proved that if one combines all possible values of the elementary errors in all possible ways, the great majority of combinations will obey the Gaussian law of errors, and for relatively few combinations will there be significant deviatio ...
Probability and Hypothesis Testing
... EXAMPLE: How many ways can an ice hockey coach assign 12 forwards to 4 forward lines (where each line consists of 3 players)? ...
... EXAMPLE: How many ways can an ice hockey coach assign 12 forwards to 4 forward lines (where each line consists of 3 players)? ...
Ars Conjectandi
Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.