chap3P3 - Introduction to Discrete Probability Discrete...

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Introduction to Discrete Probability

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Discrete Probability 2 In the real world events can not be predicted with total certainty. The best we can do is say how likely they are to happen, using the idea of probability. Tossing a Coin When a coin is tossed, there are two possible outcomes: heads (H) or tails (T) We say that the probability of the coin landing H is 1/2. Similarly, the probability of the coin landing T is 1/2. Throwing Dice When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6. The probability of throwing any one of these numbers is 1/6.
Discrete Probability 3 The theory of probability plays a crucial role in making inferences. Probability measures how likely something is to occur. Probability is the ratio of the number of favourable cases to the total number of cases, assuming that all of the various cases are equally possible. Probability of an event happening = Number of ways it can happen Total number of outcomes

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Discrete Probability Example 1 Example 2 4 The chances of rolling a "4" with a die Number of ways it can happen: 1 (there is only 1 face with a "4" on it) Total number of outcomes: 6 (there are 6 faces altogether) So the probability = 1/6 There are 5 marbles in a bag: 4 are blue, and 1 is red. What is the probability that a blue marble will be picked? Number of ways it can happen: 4 (there are 4 blues) Total number of outcomes: 5 (there are 5 marbles in total) So the probability = 4/5 = 0.8
Discrete Probability 5 You can show probability on a Probability Line: The probability is always between 0 and 1 The probability of an event occurring is somewhere between impossible and certain. As well as words we can use numbers (such as fractions or decimals) to show the probability of something happening: Impossible is zero Certain is one .

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Discrete Probability - Terminology 6 Experiment A repeatable procedure that yields one of a given set of outcomes Tossing a coin, throwing dice, seeing what pizza people choose Sample space The range of outcomes possible For a die, that would be values 1 to 6 Event One of the sample outcomes that occurred Getting a Tail when tossing a coin An event can include one or more possible outcomes Rolling an "even number" (2, 4 or 6) is also an event
Discrete Probability - Definition The probability of an event occurring is: Where E is the set of desired events (outcomes) S is the set of all possible events (outcomes) Note that 0 ≤ |E| ≤ |S| Thus, the probability will always between 0 and 1 An event that will never happen has probability 0 An event that will always happen has probability 1 S E E P ) ( 7

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Discrete Probability 8 Question: What is the probability of picking a red marble out of a bowl with 2 red and 8 brown?
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