Investigation 1 Review
... According to the National Center for Education Statistics, the percentage of students who are homeschooled in the United States is 2.2 percent. If you pick 5 students at random in the United States, what is the probability that they are all homeschooled? ...
... According to the National Center for Education Statistics, the percentage of students who are homeschooled in the United States is 2.2 percent. If you pick 5 students at random in the United States, what is the probability that they are all homeschooled? ...
Probability of Independent Events
... A number cube is rolled and the spinner is spun. Find the probability of rolling an even number and spinning a 4. ...
... A number cube is rolled and the spinner is spun. Find the probability of rolling an even number and spinning a 4. ...
Name________________________________
... 8. When Joe bowls, he can get a strike (knock down all the pins) 60% of the time. How many times more likely is it for Joe to bowl at least three strikes out of four tries as it is for him to bowl zero strikes out of four tries? Round your answer to the nearest whole number. ...
... 8. When Joe bowls, he can get a strike (knock down all the pins) 60% of the time. How many times more likely is it for Joe to bowl at least three strikes out of four tries as it is for him to bowl zero strikes out of four tries? Round your answer to the nearest whole number. ...
Simple Finite Probability Sample Space S: The set of possible
... Ex: the prob. that a length 10 bit string begins in 1 given exactly 2 1s is C(9, 1)/C(10, 2). E1 and E2 are independent if and only if p(E1 ∩ E2) = p(E1)p(E2) Example: Two dice adding up to 7 is independent of the first die being even. p(E1 ∩ E2) = 3/36, P (E1) = 6/36, P (E2) = 18/36. Example: I rep ...
... Ex: the prob. that a length 10 bit string begins in 1 given exactly 2 1s is C(9, 1)/C(10, 2). E1 and E2 are independent if and only if p(E1 ∩ E2) = p(E1)p(E2) Example: Two dice adding up to 7 is independent of the first die being even. p(E1 ∩ E2) = 3/36, P (E1) = 6/36, P (E2) = 18/36. Example: I rep ...
Sampling Theory • sample space set of all possible outcomes of a
... set of all possible outcomes of a chance experiment • event set of one or more outcomes from the sample space • probability model method for assigning probabilities to the outcomes in a sample space • disjoint events events which have no outcomes in common, that is, can never occur simultaneously Ru ...
... set of all possible outcomes of a chance experiment • event set of one or more outcomes from the sample space • probability model method for assigning probabilities to the outcomes in a sample space • disjoint events events which have no outcomes in common, that is, can never occur simultaneously Ru ...
Exercise 4
... 5. Thirty percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions. (a) Let X= the number of the six customers who will make a purchase. Write the binomial formula for this situation. (b) Wh ...
... 5. Thirty percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions. (a) Let X= the number of the six customers who will make a purchase. Write the binomial formula for this situation. (b) Wh ...
Probability interpretations
The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical tendency of something to occur or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory.There are two broad categories of probability interpretations which can be called ""physical"" and ""evidential"" probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. In such systems, a given type of event (such as the dice yielding a six) tends to occur at a persistent rate, or ""relative frequency"", in a long run of trials. Physical probabilities either explain, or are invoked to explain, these stable frequencies. Thus talking about physical probability makes sense only when dealing with well defined random experiments. The two main kinds of theory of physical probability are frequentist accounts (such as those of Venn, Reichenbach and von Mises) and propensity accounts (such as those of Popper, Miller, Giere and Fetzer).Evidential probability, also called Bayesian probability (or subjectivist probability), can be assigned to any statement whatsoever, even when no random process is involved, as a way to represent its subjective plausibility, or the degree to which the statement is supported by the available evidence. On most accounts, evidential probabilities are considered to be degrees of belief, defined in terms of dispositions to gamble at certain odds. The four main evidential interpretations are the classical (e.g. Laplace's) interpretation, the subjective interpretation (de Finetti and Savage), the epistemic or inductive interpretation (Ramsey, Cox) and the logical interpretation (Keynes and Carnap).Some interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing. The physical interpretation, for example, is taken by followers of ""frequentist"" statistical methods, such as R. A. Fisher, Jerzy Neyman and Egon Pearson. Statisticians of the opposing Bayesian school typically accept the existence and importance of physical probabilities, but also consider the calculation of evidential probabilities to be both valid and necessary in statistics. This article, however, focuses on the interpretations of probability rather than theories of statistical inference.The terminology of this topic is rather confusing, in part because probabilities are studied within a variety of academic fields. The word ""frequentist"" is especially tricky. To philosophers it refers to a particular theory of physical probability, one that has more or less been abandoned. To scientists, on the other hand, ""frequentist probability"" is just another name for physical (or objective) probability. Those who promote Bayesian inference view ""frequentist statistics"" as an approach to statistical inference that recognises only physical probabilities. Also the word ""objective"", as applied to probability, sometimes means exactly what ""physical"" means here, but is also used of evidential probabilities that are fixed by rational constraints, such as logical and epistemic probabilities.It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.