Logical fallacy
... A logical fallacy is an error in logical argument which is independent of the truth of the premises. It is a flaw in the structure of an argument as opposed to an error in its premises. When there is a fallacy in an argument it is said to be invalid. The presence of a logical fallacy in an argument ...
... A logical fallacy is an error in logical argument which is independent of the truth of the premises. It is a flaw in the structure of an argument as opposed to an error in its premises. When there is a fallacy in an argument it is said to be invalid. The presence of a logical fallacy in an argument ...
Proof Assignment #7 1. You and the bank play the following game
... According to the Binomial Theorem, this last sum is equivalent to (1 + 12 )n . Hence, a fair price for the ticket would be ( 23 )n dollars. (b)[1 point] Prove: The probability that you break even (i.e. receive at least your ticket’s worth) is exponentially small. (Hint: At least how many “heads” do ...
... According to the Binomial Theorem, this last sum is equivalent to (1 + 12 )n . Hence, a fair price for the ticket would be ( 23 )n dollars. (b)[1 point] Prove: The probability that you break even (i.e. receive at least your ticket’s worth) is exponentially small. (Hint: At least how many “heads” do ...
At the Super Roulette Game, Alison has to spin the wheel
... Lisa draws 2 candies in succession without putting the first one back into the jar. What is the probability that she draws a black candy followed by a green one? ...
... Lisa draws 2 candies in succession without putting the first one back into the jar. What is the probability that she draws a black candy followed by a green one? ...
Lab. 3
... We know that the random variable Y has a binomial distribution with parameters p = 0.5 and n = 100. We show that for sufficiently large n (usually n> 30), we can use the normal distribution N ( m, ) tables instead of the binomial distribution tables. To do this, first generate the table for this b ...
... We know that the random variable Y has a binomial distribution with parameters p = 0.5 and n = 100. We show that for sufficiently large n (usually n> 30), we can use the normal distribution N ( m, ) tables instead of the binomial distribution tables. To do this, first generate the table for this b ...
Review of Probability and Binomial Distributions
... • Should you accept the bet? • What is your expected return on this bet? • How can we calculate the odds? ...
... • Should you accept the bet? • What is your expected return on this bet? • How can we calculate the odds? ...
Thinking about probability…
... random – when individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions probability – a number between 0 and 1 that describes the proportion of times an outcome would occur in a very long series of repetitions Random in statistics does not mea ...
... random – when individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions probability – a number between 0 and 1 that describes the proportion of times an outcome would occur in a very long series of repetitions Random in statistics does not mea ...
Independent Events Two events are said to be independent if the
... The law of multiplication for conditional probabilities says P (A and B) = P (A) × P (B | A). Note that if we just interchange the role of A and B, we also get P (A and B) = P (B) × P (A | B). Finally, if A and B are independent, we get P (A | B) = P (A) and P (B | A) = P (B) — that formalizes what ...
... The law of multiplication for conditional probabilities says P (A and B) = P (A) × P (B | A). Note that if we just interchange the role of A and B, we also get P (A and B) = P (B) × P (A | B). Finally, if A and B are independent, we get P (A | B) = P (A) and P (B | A) = P (B) — that formalizes what ...
6.1 Discrete vs Continuous Random Variables
... Example 2: Another wager players can make in roulette is called a “corner bet”. To make this bet, a player places his chips on the intersection of four numbered squares on the roulette table. If one of these numbers comes up on the wheel and the player bet $1, the player gets his $1 back plus $8 mor ...
... Example 2: Another wager players can make in roulette is called a “corner bet”. To make this bet, a player places his chips on the intersection of four numbered squares on the roulette table. If one of these numbers comes up on the wheel and the player bet $1, the player gets his $1 back plus $8 mor ...
Perceptions of Randomness: Why Three Heads Are Better Than Four
... of randomness are so poor? Can people’s undoubted sensitivity to the structure of the environment be reconciled with these seeming errors of judgment? We propose that the answer to this question is yes: There is a simple way in which people’s supposed misperceptions reflect environmental statistics ...
... of randomness are so poor? Can people’s undoubted sensitivity to the structure of the environment be reconciled with these seeming errors of judgment? We propose that the answer to this question is yes: There is a simple way in which people’s supposed misperceptions reflect environmental statistics ...
Probability
... • These notes are not complete, but they should help in organizing the class flow. • Please augment these notes with your own sketches and math. You need to actively participate. • It is virtually impossible to learn this from a verbal description or these ppt bullet points. You must create your own ...
... • These notes are not complete, but they should help in organizing the class flow. • Please augment these notes with your own sketches and math. You need to actively participate. • It is virtually impossible to learn this from a verbal description or these ppt bullet points. You must create your own ...
Problem Sheet 1
... outcome of the red die. Let Y denote the outcome of the red die and denote by X the sum of the outcomes on the blue die. a) Find E(X) and V ar(X). b) What is the sign of cov(X, Y )? 6. Some years ago I met an old fisherman. He was fishing in a big lake, in which many small fish were swimming regardl ...
... outcome of the red die. Let Y denote the outcome of the red die and denote by X the sum of the outcomes on the blue die. a) Find E(X) and V ar(X). b) What is the sign of cov(X, Y )? 6. Some years ago I met an old fisherman. He was fishing in a big lake, in which many small fish were swimming regardl ...
Probability
... • These notes are not complete, but they should help in organizing the class flow. • Please augment these notes with your own sketches and math. You need to actively participate. • It is virtually impossible to learn this from a verbal description or these ppt bullet points. You must create your own ...
... • These notes are not complete, but they should help in organizing the class flow. • Please augment these notes with your own sketches and math. You need to actively participate. • It is virtually impossible to learn this from a verbal description or these ppt bullet points. You must create your own ...
Probability Statistics Student Module
... In her rush to get to her job, Rosa forgets to take her umbrella about 30% of the time. If the weatherman says there is a 70% chance of rain, what is the probability that it rains and she left the umbrella at home? ...
... In her rush to get to her job, Rosa forgets to take her umbrella about 30% of the time. If the weatherman says there is a 70% chance of rain, what is the probability that it rains and she left the umbrella at home? ...
16 Conditional Probability
... Trial processes. In many situations, a probabilistic experiment is repeated, possibly many times. We call this a trial process. It is independent if the i-th trial is not influenced by the outcomes of the preceding i − 1 trials, that is, ...
... Trial processes. In many situations, a probabilistic experiment is repeated, possibly many times. We call this a trial process. It is independent if the i-th trial is not influenced by the outcomes of the preceding i − 1 trials, that is, ...
A survey of probability concepts • Objective probability: classical and
... executives were surveyed about their loyalty to their company. One of the questions was, “If you were given an offer by another company equal to or slightly better than your present position, would you remain with the company or take the other position?” The responses of the 200 executives in the su ...
... executives were surveyed about their loyalty to their company. One of the questions was, “If you were given an offer by another company equal to or slightly better than your present position, would you remain with the company or take the other position?” The responses of the 200 executives in the su ...
Unit 2 Statistics and Experimental Probability
... Learning Goals:– I can compare the theoretical probability of an event with the experimental probability, and explain why they might differ And I can determine, through investigation the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment ...
... Learning Goals:– I can compare the theoretical probability of an event with the experimental probability, and explain why they might differ And I can determine, through investigation the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment ...
Economics for Business
... 20% of the time. Now what is your best strategy? Call Heads brings you 80%x1+20%x(-1)=0.6. Call Tails gives you 0.2x1+0.8x(-1)=-0.6. So best strategy is to call Heads. ...
... 20% of the time. Now what is your best strategy? Call Heads brings you 80%x1+20%x(-1)=0.6. Call Tails gives you 0.2x1+0.8x(-1)=-0.6. So best strategy is to call Heads. ...
Chapter 5.3
... Survey on Fear of Being Home Alone at Night Public Opinion reported that 5% of Americans are afraid of being alone in a house at night. If a random sample of 20 Americans is selected, find these probabilities. 1. There are exactly five people in the sample who are afraid of being alone at night 2 ...
... Survey on Fear of Being Home Alone at Night Public Opinion reported that 5% of Americans are afraid of being alone in a house at night. If a random sample of 20 Americans is selected, find these probabilities. 1. There are exactly five people in the sample who are afraid of being alone at night 2 ...
5.1 Heads or tails
... Teacher: Probability is the likelihood of something occurring and statistics is a fact or piece of information that is expressed as a number or percentage. What is the probability of tossing this coin and it landing on heads or tails? Students: Allow students to give their opinions B. Explanation: ...
... Teacher: Probability is the likelihood of something occurring and statistics is a fact or piece of information that is expressed as a number or percentage. What is the probability of tossing this coin and it landing on heads or tails? Students: Allow students to give their opinions B. Explanation: ...
Gambler's fallacy
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future (presumably as a means of balancing nature). In situations where what is being observed is truly random (i.e., independent trials of a random process), this belief, though appealing to the human mind, is false. This fallacy can arise in many practical situations although it is most strongly associated with gambling where such mistakes are common among players.The use of the term Monte Carlo fallacy originates from the most famous example of this phenomenon, which occurred in a Monte Carlo Casino in 1913.