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Ch6 Probability.pdf

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Department
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Nabil Ayoub
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Winter

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Chapter 6: Probability Appendix B Introdution into Probability Counting Rules for Multiple-Step Experiments: If an experiment can be described as a sequence of k steps with n1possible outcomes on the first step, n2possible outcomes on the second step, and so on, then the total number of experimental outcomes is given by (1 ) 2n )3(n )…k(n ).  Flip of a Coin, Two Coins, and Three Coins: the possible outcomes? ______ ____________  Ontario automobile license plates (in general) are composed of four letters followed by three numbers, the total possible outcomes (license plates) ____________  A billiard of 10 balls, each has a number from 0 to 9, form a number contains 10 digits. The possible outcomes (different numbers can be formed) ____________  From a group of 4 colors, form a set of 3 colors. Total possible outcomes: COMBINATIONS: ____________ PERMUTATIONS: ____________ 6.1 Assigning Probability to Events  RANDOM EXPERIMENT is an action or process that leads to one of several possible outcomes. o Exhaustive Outcomes: List of all possible outcomes. o Mutually Exclusive: any two outcomes cannot occur at the same time.  SAMPLE SPACE of a random experiment is a list of all possible outcomes of the experiment. The outcomes must be exhaustive and mutually exclusive. We use the notation S = {Q , Q 1 ..2 , Q )k to represent Sample Space & outcomes.  Requirements of Probabilities:  The probability of any outcome must lie between: ____________  The sum of the probabilities of all the outcomes in a sample space must be: ____________ Approaches to Assigning Probabilities Classical Approach: based on equally likely events.  Flip a balanced COIN: possible outcomes? Probability of each? Sum of the probabilities?  Toss of a balanced DIE: possible outcomes? Probability of each? Sum of the probabilities?  Toss of a balanced DICE: possible outcomes? Probability of each? Sum of the probabilities? Relative Frequency approach:  ex. 1000 students, 250 received “A” grade, 300 “B”, 200 “C”, 150 “D”, & 100 received “F” grade. Relative frequency? Sum of the probabilities?  Event:is a collection or set of one or more simple events (individual outcome) in a sample space. ex. P(A) P(B) P(C) P(D) P(F) P(pass) P(pass and not A) P(A or B) P(B > marks > D)  Probability of an Event: is sum of the probabilities of the simple events that constitute the event  The probability of getting head in the flip of a balanced coin is ½. So, the probability of heads in the flip of a balanced coin infinite times is ½.  The probability of getting 3 with a balanced die is ⅙. So, the probability of getting 3 with a balanced
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