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E-Chp_5

# E-Chp_5 - CHAPTER 5 PROBABILITY Introduction Probability as...

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8/3/10 CHAPTER 5 - PROBABILITY

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8/3/10 Introduction Probability as a general concept can be defined as the chance of an event occurring. In addition to being used in games of chance, probability is used in the fields of insurance, investments, and weather forecasting, and in various areas. Rules such as the fundamental counting rule, combination rule and permutation rules allow us to count the number of ways in which events can occur. Counting rules and probability rules can be used together to solve a wide variety
8/3/10 Probability language of uncertainty plays an important role in statistical inference making procedures Example: 40% chance of rain Goal Average of Fenerbahce FC 1.313 The probability of a royal flush is 1:649,740

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Click to edit Master subtitle style 8/3/10 Probability Experiments It is any process whose result is determined by chance. Examples: Roll a die. Flip a Coin. Draw a card from a shuffled deck Choose a name from a hat. Outcome – Any possible result of a probability experiment.
Click to edit Master subtitle style 8/3/10 Sample Space The collection of all possible outcomes for an experiment. The sample space is often denoted by S . Examples: The sample space of the experiment Flip a Coin has 2 outcomes heads and tails, so we could write: S={Head, Tail} The experiment of rolling a die has 6 possible outcomes 1-6, so: S={1, 2, 3, 4, 5, 6}

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Click to edit Master subtitle style 8/3/10 Event Any collection of outcomes from the sample space. We will generally use capital letters to represent events. Examples: Rolling an even number is an event for the experiment of rolling a die. If we call this event E , we could write: E={2,4,6} Drawing a king is an event for the experiment of drawing a card from a deck. If we call this event K , K contains 4 outcomes: king of hearts, king of spades, king of diamonds and king of clubs. K={king of hearts, king of spades, king of diamonds, king of clubs}
Click to edit Master subtitle style 8/3/10 Types of Probability There are three basic interpretations of probability: 1- Classical probability 2- Empirical or relative frequency probability 3- Subjective probability

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Click to edit Master subtitle style 8/3/10 1- Classical Probability Classical probability uses sample spaces to determine the numerical probability that an event will happen. (One does not actually have to perform the experiment to determine that probability). Classical probability assumes that all outcomes in the sample space are equally likely to occur. ( For example, when a single die is rolled, each outcome has the same probability of occurring. Since there are six outcomes, each outcome has a probability of 1/6.)
Click to edit Master subtitle style 8/3/10 1- Classical Probability It is used when each outcome in a sample space is equally likely to occur. When outcomes are equally likely; P(E)=n(E)/n(S) outcomes of number Total event to favorable outcomes of Number = event any of y Probabilit

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Example of Equally Likely Outcome Method When rolling a die, the probability of getting a number less than three = Obj101
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