fundamentals of probability ppt

- Computing Fundamentals 2 Lecture 6 Probability Lecturer: Patrick Browne http://www.comp.dit.ie/pbrowne/ * Two events A and B are statistically independent if the ... | PowerPoint PPT presentation | free to view. the definition – probability of an event. The Binomial Formula • I roll a die 15 times and count the number of times I roll a 3 or a 4 • What is the probability that I roll a 3 or 4 exactly 9 times? - FUNDAMENTALS OF GENETICS CHAPTER 8 GENETICS Genetics is a field of Biology that is devoted to understanding HOW characteristics are passed on from parents to offspring. • What is the probability of getting an odd number of heads? 1/52, or about 1.92% 1/51, or about 1.96% 0, “And” Statements • In general, we say the conditional probability of A occurring given that B occurs is the probability that both A and B occur, divided by the probability that B occurs in the first place. analytical geometry. randomly select a college student. And they’re ready for you to use in your PowerPoint presentations the moment you need them. - Get exhausted from searching the best probability assignment helper? outline. The Binomial Formula • We play a game where I roll a fair 6-sided die • Whatever number I roll, you flip a fair coin that many times and count the number of heads • If I haven’t rolled yet, what is the probability of getting 2 heads? powered by it scholars. The videos in Part I introduce the general framework of probability models, multiple discrete or continuous random variables, expectations, conditional distributions, and various powerful tools of general applicability. Title: Fundamentals of Probability 11'4 1 Fundamentals of Probability 11.4 Probability An event that is expressed as a number. 13/52 + 13/52 = 26/52 = 50% 12/52 + 4/52 = 16/52  30.77% 13/52 + 4/52 – 1/52 = 16/52  30.77%, “Or” Statements • Memorize these properties, and use them to your advantage, The Binomial Formula • If I flip a fair coin 1 time, the possible outcomes are heads (H) and tails (T) • If I am interested in counting heads, the possible outcomes are 1 (for heads) and 0 (for tails) • If X = number of heads… • P(X = 0) = 1/2 • P(X = 1) = 1/2, The Binomial Formula • If I flip a fair coin 2 times, the possible outcomes are HH, HT, TH, and TT • If I am interested in counting heads, the possible outcomes are 0, 1, and 2 • If X = number of heads… • P(X = 0) = 1/4 • P(X = 1) = 2/4 • P(X = 2) = 1/4, The Binomial Formula • If I flip a fair coin 3 times, the possible outcomes are HHH, HHT, HTH, THH, TTH, THT, HTT, and TTT • If I am interested in counting heads, the possible outcomes are 0, 1, 2, and 3 • If X = number of heads… • P(X = 0) = 1/8 • P(X = 1) = 3/8 • P(X = 2) = 3/8 • P(X = 3) = 1/8, The Binomial Formula • In the 3-coin case, one way of arriving at P(X = 2) is to find P(HHT) and multiply it by the number of ways to shuffle the H’s and T’s around and still have 2 heads • This works because each of the simple outcomes is equally likely • P(HHT) = P(H)P(H)P(T) = P(H)2P(T) = (1/2)2(1/2) = 1/8 • There are 3 ways to shuffle 2 heads around 3 flips • HHT, HTH, and THH • Then P(X = 2) = 3(1/8) = 3/8, The Binomial Formula • In general, the number of ways to shuffle k heads around n flips is given by the binomial coefficient • Where x! Probability of Inclusive Events If two events, A and B, are inclusive, then the probability that either A or B is the sum of their probabilities decreased by the probability of both appearing. Joint Probability Distributions - . CrystalGraphics 3D Character Slides for PowerPoint, - CrystalGraphics 3D Character Slides for PowerPoint. That's all free as well! 1. 1/6 or about 16.7% 1/6 or about 16.7%, 1 2 3 4 5 6 Simple Sample Spaces • We will often picture chance processes as a box model • Takes each possible outcome and makes a “ticket” out of it • Equally likely to draw any one ticket • In the dice context, rolling a single die could be modeled with the box • Since we are equally likely to draw any ticket, the probability of rolling any particular number is 1/6, 2 1 3 2 4 3 5 4 6 5 7 6 8 5 9 4 10 3 11 2 12 1 Simple Sample Spaces • If there is more than one of a type of ticket in the box, use superscripts to denote how many of that ticket type there are • The “sum of two dice” box model is, “And” Statements • Quite often, the probability of one outcome occurring is dependent (or conditional) on the outcome of a prior event • If I deal two cards off of a well-shuffled standard deck, I’ll give you a dollar if the second card is the queen of spades (Q♠) • If the first card hasn’t been turned over, what is the probability of winning $1? PROBABILITY! The Binomial Formula • We play a game where I roll a fair 6-sided die • Whatever number I roll, you flip a fair coin that many times and count the number of heads • Suppose I roll a 3 • What is the probability of getting 2 heads? - Chapter 9 Fundamentals of Genetics In Humans, Blood types and Sickle cell Anemia exhibit codominance 1. (4/52)(4/51)(3/50)  0.0036% (13/52)(12/51)(11/50)  1.29%, “And” Statements • Three dice are rolled. what is probability?. If a person tests positive on a ... - Chapter 2 Basics of DNA Biology and Genetics Fundamentals of Forensic DNA Typing Slides prepared by John M. Butler June 2009, PHILOSOPHY OF PROBABILITY AND ITS RELATIONSHIP (?) The PowerPoint PPT presentation: "Fundamentals of Probability 11'4" is the property of its rightful owner. To view this presentation, you'll need to allow Flash.

• It is the ratio of desired outcomes to total outcomes. Simple Sample Spaces • Possible outcomes when rolling two dice • Each singular possibility is equally likely • This is a simple sample space, Simple Sample Spaces • In this case, the probability of rolling a total number is equal to the total number of ways to get that number, divided by the number of possible outcomes • The probability that the dice total 4 is • This is because the outcomes are equally likely, Simple Sample Spaces • What is the probability the dice total 7? fundamentals. ISBN: 0-13-145340-8 1. Probability Powerpoint. Sign in. outlines two discrete/continuous random variables joint probability distributions, Chapter 6 - . developed by kaseya university. Z. y. p(X = x;Y = y)dxdy = 1. probability . - Sample Space, Events, and PROBABILITY In this chapter, we will study the topic of probability which is used in many different areas including insurance, science ... - Three DIFFERENT probability statements If a person has HIV, the probability that they will test positive on a screening test is 90%. Title. • If the first card is Q♠, what is the probability of winning $1? • We can rewrite this equation to give ourselves a general rule for finding the probability that A and B occur • Could be at once or in sequence, depending on the context • P(AB) = P(A|B)P(B), “And” Statements • In some cases, the occurrence of one event has no effect on the outcome another • Flipping a coin or rolling a die, for example • Events like these are independent • Mathematically, A and B are independent if and only if P(A|B) = P(A) • Substituting this into the rule for intersections in the previous paragraph gives us a special case rule for “and” statements • If A and B are independent, then P(AB) = P(A)P(B) • If A and B are independent, then so are their complements, “And” Statements • If I deal 3 cards off of a well-shuffled standard deck… • What is the probability that the first card is an ace, the second card is a jack, and the third card is another ace? If I flip a coin 50 times, what is the probability of heads? 1 denotes an event that is certain to occur. Summary • A probability is a numerical value assigned to an event to quantify the likelihood of that event’s occurrence • Probabilities are always between 0 and 1 • A probability of 1 denotes a “sure thing” • Probabilities are usually determined by a combination of counting methods and use of formulae governing logical statements • Or • And • Not, Summary • If a game’s outcomes are broken down into equally likely simple events, the probability a general event occurs is equal to the number of simple events satisfying the conditions, divided by the total possible number of simple events, Summary • If the probability of one event is determined in part by knowledge of another event, we say those events are conditional • Otherwise, the events are independent • If two events cannot occur simultaneously, we say the events are mutually exclusive, Summary • Most problems you will encounter have the following format • An event is given that we are interested in finding the probability for • This event will be some combination of unions, intersections, and complements of simpler events that we can calculate • By using the rules and properties from this section, we can rewrite the probability we were initially interested in in terms of the simpler probabilities • In a sense, you create a formula for each problem from the building blocks learned in this section, Summary • If you play a sequence of n independent games and count the number of wins, the binomial formula gives the probability of winning exactly k out of n games, © 2020 SlideServe | Powered By DigitalOfficePro, - - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -.