Probability Teasers 1. A family has 2 children. We pick one child and
... The ANSWERS Answer a) is wrong because it determines the probability of 2 boys, not the probability that both are boys given one is. Thus, this answer leaves out some important information-- the fact that you know one child is a boy. This information destroys the "equally likely" assumption. You ca ...
... The ANSWERS Answer a) is wrong because it determines the probability of 2 boys, not the probability that both are boys given one is. Thus, this answer leaves out some important information-- the fact that you know one child is a boy. This information destroys the "equally likely" assumption. You ca ...
slides
... Independence of events Independent objects = not connected with each other, not influencing each other Example: Roll 2 dice, let B := {first is 1 or 4} and C := {second is 3}. ...
... Independence of events Independent objects = not connected with each other, not influencing each other Example: Roll 2 dice, let B := {first is 1 or 4} and C := {second is 3}. ...
Document
... without replacement from a bag of 28 marbles in which there are 7 red, 7 black, 7 blue, & 7 white. What is the probability that 2 are of one color and 3 are of another color? P(3 one color, 2 another) = s s+f = (2 colors from 4)(2 same from 7)(3 same from 7) total possible = (4 nPr 2)(7 nCr 2)(7 nCr ...
... without replacement from a bag of 28 marbles in which there are 7 red, 7 black, 7 blue, & 7 white. What is the probability that 2 are of one color and 3 are of another color? P(3 one color, 2 another) = s s+f = (2 colors from 4)(2 same from 7)(3 same from 7) total possible = (4 nPr 2)(7 nCr 2)(7 nCr ...
Section 11.1 The Fundamental Counting Principle
... • Complement of E: If we know P(E), the probability of an event E, we can determine the probability that the event will not occur, denoted by P(not E). • The probability that an event E will not occur is equal to 1 minus the probability that it will occur. P(not E) = 1 – P(E) • The probability that ...
... • Complement of E: If we know P(E), the probability of an event E, we can determine the probability that the event will not occur, denoted by P(not E). • The probability that an event E will not occur is equal to 1 minus the probability that it will occur. P(not E) = 1 – P(E) • The probability that ...
Document
... If event A can occur in n1 ways and event B can occur in n2 ways, then events A and B can occur in n1 x n2 ways. ...
... If event A can occur in n1 ways and event B can occur in n2 ways, then events A and B can occur in n1 x n2 ways. ...
PART TWO PROBABILITY I. Counting
... countable or can represented as whole numbers. Examples: number of automobile accidents per year, number of defective items per year, number of eggs laid each month by a hen. 2.Continuous Random Variables – random variables that can take on values on a continuous scale. Examples: length of time to p ...
... countable or can represented as whole numbers. Examples: number of automobile accidents per year, number of defective items per year, number of eggs laid each month by a hen. 2.Continuous Random Variables – random variables that can take on values on a continuous scale. Examples: length of time to p ...
Overall
... several clusters, a reporting period, or a school year. These can also be used in place of the Unit Summary. ...
... several clusters, a reporting period, or a school year. These can also be used in place of the Unit Summary. ...
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.