5. Discrete Probability

# 5. Discrete Probability - 8/27/09 11 8/27/09 MATH 224 –...

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Unformatted text preview: 8/27/09 11 8/27/09 MATH 224 – Discrete Mathematics Basic finite probability is given by the formula , where | E | is the number of events and |S| is the total number of possible outcomes. This definition assumes that each event is equally likely. In other words each even has probability 1/|E| . Basics of Discrete Probability | | | | ) ( S E E P = So for example, if we want the probability of tossing a coin four times where the first two times the coin comes up heads followed by two tails, this set E has only one element. The set of all possible 4-coin tosses is 2 4 . So the probability of two heads followed by two tails is 1/16 . On Page 394 of the textbook, there is a container with four blue balls and five red balls. What is the probability of choosing a blue ball when selecting one ball? The answer is 4/9. 8/27/09 22 8/27/09 MATH 224 – Discrete Mathematics Now consider what happens when rolling a fair die. The probability of rolling any of the values between one and six is 1/6. When rolling two dice the probabilities are: P(2) = P(12) = 1/36 since there is only one way to get a 2 (two ones). P(3) = P(11) = 2/36 = 1/18 since there are two ways of getting a 3 (2 and 1 or 1 and a 2) P(4) = P(10) = 3/36 = 1/12 What are the three ways of getting four? P(5) = P(9) = 4/36 = 1/9 P(6) = P(8) = 5/36 P(7) = 6/36 = 1/6 Why is the denominator 36? The sum of theses probabilities is 2(1/36)+2(2/36)+2(3/36)+2(4/36)+2(5/36)+(6/36) = 36/36 =1. Do the set of all probabilities always sum to 1? Probability 8/27/09 33 8/27/09 MATH 224 – Discrete Mathematics Often counting the number of different events can be difficult or tricky. Consider Example 6 from our text. First determine the number of different 5-card hands in poker in order to get the denominator...
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## This note was uploaded on 08/26/2009 for the course MATH 224 taught by Professor Waxman during the Fall '08 term at Southern Illinois University Edwardsville.

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5. Discrete Probability - 8/27/09 11 8/27/09 MATH 224 –...

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