Probability theory and average
... • Idea: “average” value of the random variable • Remember: random variable X is a mapping from events in a sample space S to numbers • Defn: Expected value of X = E X = Pr = ...
... • Idea: “average” value of the random variable • Remember: random variable X is a mapping from events in a sample space S to numbers • Defn: Expected value of X = E X = Pr = ...
Article Reflection #2
... intuitions typically contradict accepted theory on these topics. The article highlights three major findings from the author’s research. The first finding was that students have their own theories or perceptions prior to instruction in probability and statistics and these theories and perceptions ar ...
... intuitions typically contradict accepted theory on these topics. The article highlights three major findings from the author’s research. The first finding was that students have their own theories or perceptions prior to instruction in probability and statistics and these theories and perceptions ar ...
Notes - Algebra II
... b) Find the probability of getting two girls:___________________________________ c) Find the probability of getting exactly one child of each gender:______________________ 3. A couple plans to have four children. a) List all the outcomes according to gender of each child (sample space). ...
... b) Find the probability of getting two girls:___________________________________ c) Find the probability of getting exactly one child of each gender:______________________ 3. A couple plans to have four children. a) List all the outcomes according to gender of each child (sample space). ...
Finding Binomial Probabilities
... Example 1: Blood type is inherited. If both parents carry genes for the O and A blood types, each child has a probability of 0.25 of getting two O genes and so of having blood type O. The number of O blood types amongst 5 children of these parents is the count, x, of successes in 5 independent obser ...
... Example 1: Blood type is inherited. If both parents carry genes for the O and A blood types, each child has a probability of 0.25 of getting two O genes and so of having blood type O. The number of O blood types amongst 5 children of these parents is the count, x, of successes in 5 independent obser ...
Statistics 262
... 3. A multiple-choice quiz has three questions, each with five answer choices. Only one of the choices is correct. You have no idea what the answer is to any question and have to guess each answer. a) Find the probability of answering the first question correctly. ...
... 3. A multiple-choice quiz has three questions, each with five answer choices. Only one of the choices is correct. You have no idea what the answer is to any question and have to guess each answer. a) Find the probability of answering the first question correctly. ...
Math 55 “Coins” Dice - People @ EECS at UC Berkeley
... 21. If eight rooks are randomly placed on a chessboard, compute the probability that none of them can capture any other. In other words, what is the probability that no two are on the same row or file? 22. Two balls are painted either blue or gold. Suppose each is painted blue with probability that ...
... 21. If eight rooks are randomly placed on a chessboard, compute the probability that none of them can capture any other. In other words, what is the probability that no two are on the same row or file? 22. Two balls are painted either blue or gold. Suppose each is painted blue with probability that ...
Harvard University
... calculate the probability that you will win after rolling a 4 for the first time. Solution. ...
... calculate the probability that you will win after rolling a 4 for the first time. Solution. ...
Section 4.4
... • If all hands are equally likely, the probability of a hand NOT containing a particular card is the quotient of: – probability of picking 5 cards from the 51 remaining: C(51,5) and – probability of picking any 5 cards from entire deck: C(52,5) ...
... • If all hands are equally likely, the probability of a hand NOT containing a particular card is the quotient of: – probability of picking 5 cards from the 51 remaining: C(51,5) and – probability of picking any 5 cards from entire deck: C(52,5) ...
problems
... However, the twelve strings are not mutually exclusive, so that many of the outcomes have been counted doubly, trebly, and so forth. Equation (1) can be corrected for the presence of two and three strings simultaneously by computing ...
... However, the twelve strings are not mutually exclusive, so that many of the outcomes have been counted doubly, trebly, and so forth. Equation (1) can be corrected for the presence of two and three strings simultaneously by computing ...
Worksheet #2 Theoretical Probability
... b. Adjust the cost of playing the game to make it fair. ...
... b. Adjust the cost of playing the game to make it fair. ...
Experimental Probability Vs. Theoretical Probability
... Law of the Large Numbers 101 • The Law of Large Numbers was first published in 1713 by Jocob Bernoulli. • It is a fundamental concept for probability and statistic. • This Law states that as the number of trials increase, the experimental probability will get closer and closer to the theoretical pr ...
... Law of the Large Numbers 101 • The Law of Large Numbers was first published in 1713 by Jocob Bernoulli. • It is a fundamental concept for probability and statistic. • This Law states that as the number of trials increase, the experimental probability will get closer and closer to the theoretical pr ...
Powerpoint
... • The events of interest are usually events that cannot be replicated easily or cannot be modeled with the equally likely outcomes approach. • As such, these values will most likely vary from person to person. • The only rule for a subjective probability is that the probability of the event must be ...
... • The events of interest are usually events that cannot be replicated easily or cannot be modeled with the equally likely outcomes approach. • As such, these values will most likely vary from person to person. • The only rule for a subjective probability is that the probability of the event must be ...
Review and Intro to Probability
... P(Raise) = probability that JoJo will get a raise P(75) = probability that exam score will be 75 ...
... P(Raise) = probability that JoJo will get a raise P(75) = probability that exam score will be 75 ...
Unit 13: Probability Rules.docx
... G. SCP.7 Apply the Addition Rule, P(A or B) = P(A)+P(B)-P(A and B), and interpret the answer in terms of the model. G.SCP 2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use the characterization to deter ...
... G. SCP.7 Apply the Addition Rule, P(A or B) = P(A)+P(B)-P(A and B), and interpret the answer in terms of the model. G.SCP 2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use the characterization to deter ...
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.