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Probability-F09 - Chapter 3 Probability C HAPTER 3...

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Chapter 3 Probability 39 HAPTER 3 I. WHAT IS PROBABILITY? Random Experiments The weatherman on 10 o’clock news program states that there is a 20% chance that it will snow tomorrow, a 65% chance that it will rain and a 15% chance that the weather will be clear. What does this mean? What are the chances that it will not rain tomorrow? What are the chances that there will be some form of precipitation? Assuming that it will either snow, rain or be clear, which of the three will occur? The table below shows the results of a recent poll of 1000 Americans on the President’s economic policies: Strongly approve 32% Mildly approve 17% Mildly disapprove 14% Strongly disapprove 23% No opinion 14% If a person is selected at random from the set of people who were polled, what is the likelihood that the person approved of the President’s economic policies? What is the likelihood that the person did not disapprove? An ordinary die is rolled. What is the likelihood that the number that turns up is a prime number? What are the chances that the number that turns up is not greater than 4? A two-headed coin is flipped. What is the likelihood that the coin will come up heads? Tails? Processes in which there are an observable set of possible outcomes are called experiments . There are two basic types of experiments. In the first three examples above, we do not know in advance what the outcome will be. We do not know for certainty what the weather will be tomorrow. If we pick a person at random from the poll group, we would C PROBABILITY PROBABILITY
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Chapter 3 Probability 40 have no way of knowing in advance what the person’s preference will turn out to be. In contrast, if we flip a two-headed coin we do know for sure what the result will be, heads! An experiment in which any one of number of possible outcomes may result is called a random experiment or probability experiment . In contrast, a process in which the outcome is known in advance (e.g., flipping a two-headed coin) is called a deterministic experiment . Probability is the branch of mathematics that is concerned with “modeling” random experiments. That is, probability attempts to provide mathematical formulations (mathematical models) of random experiments. Since we will be concerned only with random experiments in the work that follows, the word experiment will mean random experiment. Sample Spaces Suppose we perform an experiment. The set S of possible outcomes is called the sample space for the experiment. Examples 1.1: List, or describe, the sample space for each experiment. 1. Roll an ordinary die and record the number of dots on the upper face. 2. Draw a card from a standard 52-card deck and record its suit. 3. Draw a card from a standard deck. 4. Toss a fair coin. If the result is “heads”, stop. If the result is “tails”, toss the coin a second time.
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